NCERT Solutions Class 3 Maths Chapter 5 Fun with Shapes
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NCERT Solutions Class 3 Maths Chapter 5 Fun with Shapes – Text
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Page 1
F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T
C L A S S 3 · M AT H S
NCERT Solutions + ×
Chapter 5: Fun with
Shapes
NCERT Textbook — Maths Mela
BOOK PAGES SECTIONS QUESTIONS MEDIUM
44 – 63 19 82 English
Every question Step by step Exam ready
Activities, in-text questions The working shown, not Written to match how
and all exercises. just the final answer. marks are awarded.
Solutions, notes, sample papers & more at 100 pages
C L A S S 3 · M AT H S
NCERT Solutions + ×
Chapter 5: Fun with
Shapes
NCERT Textbook — Maths Mela
BOOK PAGES SECTIONS QUESTIONS MEDIUM
44 – 63 19 82 English
Every question Step by step Exam ready
Activities, in-text questions The working shown, not Written to match how
and all exercises. just the final answer. marks are awarded.
Solutions, notes, sample papers & more at 100 pages
Page 2
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
C L A SS 3 · M AT H S · M AT H S M E L A
NCERT So ut ons — C apt r 5: Fun w t S ap s
l i h e i h h e
This chapter is full of shapes. You copy Ammaʼs rangoli on dots, open a box and trace its faces, and get to
know the square, the rectangle, the triangle and the circle.
T E XT B OOK B OOK PAGE S
Ma h Mela Cla
t s ss 3 44 63
S EC T I ONS QU E ST I ONS
19 82
M EDI UM
English
Let us Do — Page 44–45 s
Ammaʼs rangoli
L E T US D O
Q1 Make Amma s rangoli on the dots given below
ʼ .
Amma s rangoli
ʼ your dots — draw here
Amma s rangoli on the left and an empty grid of dots on the right
ʼ .
Copy Amma s rangoli dot by dot
ʼ .
An orange square at each corner.
Page 1 of 100
gl e l i
C L A SS 3 · M AT H S · M AT H S M E L A
NCERT So ut ons — C apt r 5: Fun w t S ap s
l i h e i h h e
This chapter is full of shapes. You copy Ammaʼs rangoli on dots, open a box and trace its faces, and get to
know the square, the rectangle, the triangle and the circle.
T E XT B OOK B OOK PAGE S
Ma h Mela Cla
t s ss 3 44 63
S EC T I ONS QU E ST I ONS
19 82
M EDI UM
English
Let us Do — Page 44–45 s
Ammaʼs rangoli
L E T US D O
Q1 Make Amma s rangoli on the dots given below
ʼ .
Amma s rangoli
ʼ your dots — draw here
Amma s rangoli on the left and an empty grid of dots on the right
ʼ .
Copy Amma s rangoli dot by dot
ʼ .
An orange square at each corner.
Page 1 of 100
Page 3
l h h e i h h e A aS m · NCERT So ut ons
A green triangle in the middle of each side.
Four blue circles in between.
A big yellow square in the middle, standing on a corner.
A small red square inside it.
− Exp anat on
l i
Why The dots hold every shape in its right place so your rangoli looks like
: ,
Ammaʼs. Count the dots before you draw each shape.
Page 2 of 100
A green triangle in the middle of each side.
Four blue circles in between.
A big yellow square in the middle, standing on a corner.
A small red square inside it.
− Exp anat on
l i
Why The dots hold every shape in its right place so your rangoli looks like
: ,
Ammaʼs. Count the dots before you draw each shape.
Page 2 of 100
Page 4
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Q2 Name the shapes drawn in Amma s rangoli
ʼ : _____________, _____________, _____________
Amma s rangoli drawn on a grid of dots
ʼ , .
The three shapes are square, triangle and circle.
The orange shapes at the corners are squares.
The green shapes are triangles.
The blue shapes are circles.
Page 3 of 100
gl e l i
Q2 Name the shapes drawn in Amma s rangoli
ʼ : _____________, _____________, _____________
Amma s rangoli drawn on a grid of dots
ʼ , .
The three shapes are square, triangle and circle.
The orange shapes at the corners are squares.
The green shapes are triangles.
The blue shapes are circles.
Page 3 of 100
Page 5
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
− Exp anat onl i
o m l a se
T p Tmhe .cbig yellow shape and the small red shape are squareasgtoo They are
a seturned to stand on a corner
i : .
ag l
just .
. com ag
a s em
Q3 How many shapes are madeagwlith a Curved lines ( ) ______________ ( b) Straight lines
m
______________
co
e m.
m l as
m .co a g
l a se
a g
m a s
m.co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
Amma s rangoli drawn on a grid of dots
m a s e
agl
ʼ , .
. co
e m
g l as
A NSW E R a
a) Curved lines: 4 — the four blue circles.
co m
(
m .
m ase
.co
a g l Page 4 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
− Exp anat onl i
o m l a se
T p Tmhe .cbig yellow shape and the small red shape are squareasgtoo They are
a seturned to stand on a corner
i : .
ag l
just .
. com ag
a s em
Q3 How many shapes are madeagwlith a Curved lines ( ) ______________ ( b) Straight lines
m
______________
co
e m.
m l as
m .co a g
l a se
a g
m a s
m.co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
Amma s rangoli drawn on a grid of dots
m a s e
agl
ʼ , .
. co
e m
g l as
A NSW E R a
a) Curved lines: 4 — the four blue circles.
co m
(
m .
m ase
.co
a g l Page 4 of 100
Page 6
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
b) Straight lines: 10.
(
4 squares + 4 triangles + 1 big square + 1 small square = 10
− Exp anat on
l i
Why A circle is drawn with one curved line Every other shape here is drawn
: .
with straight lines only: 4 orange squares, 4 green triangles, the big yellow
square and the small red square.
Q4 Use cut outs of shapes to make a rangoli design Outline the object and colour
. .
Sample answer:
Cut squares, triangles and circles from coloured paper.
Arrange them on a sheet as a pretty design.
Draw around each cut-out with a pencil.
Lift the cut-outs and colour inside the outlines.
Try this: Make the same design twice, once small and once big.
Page 5 of 100
gl e l i
b) Straight lines: 10.
(
4 squares + 4 triangles + 1 big square + 1 small square = 10
− Exp anat on
l i
Why A circle is drawn with one curved line Every other shape here is drawn
: .
with straight lines only: 4 orange squares, 4 green triangles, the big yellow
square and the small red square.
Q4 Use cut outs of shapes to make a rangoli design Outline the object and colour
. .
Sample answer:
Cut squares, triangles and circles from coloured paper.
Arrange them on a sheet as a pretty design.
Draw around each cut-out with a pencil.
Lift the cut-outs and colour inside the outlines.
Try this: Make the same design twice, once small and once big.
Page 5 of 100
Page 7
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Q5 Try to make the following objects using shape cutouts .
boat butterfly rocket
Three pictures made by joining cut-out shapes.
Match your cut-outs to the pictures.
Boat: rectangle triangles small squares
1 , 4 , 3 .
Butterfly: triangles for wings a circle and an oval for the body
2 , , 2 small circles.
Rocket: rectangle triangles small circles and a half circle
1 , 3 , 2 .
− Exp anat on
l i
Boat: the long rectangle is the body with a triangle at each end Two triangles make the
, .
sails. Three small squares are the windows.
Butterfly: two triangles are the wings. A circle and an oval make the body. Two small
black circles sit near the head.
Rocket: one triangle is the tip and one rectangle is the body. Two triangles are the fins.
Two small circles are the windows. A half circle is at the bottom.
Why Big pictures can be built out of a few simple shapes
: .
Let us Do — Page 46
Page 6 of 100
gl e l i
Q5 Try to make the following objects using shape cutouts .
boat butterfly rocket
Three pictures made by joining cut-out shapes.
Match your cut-outs to the pictures.
Boat: rectangle triangles small squares
1 , 4 , 3 .
Butterfly: triangles for wings a circle and an oval for the body
2 , , 2 small circles.
Rocket: rectangle triangles small circles and a half circle
1 , 3 , 2 .
− Exp anat on
l i
Boat: the long rectangle is the body with a triangle at each end Two triangles make the
, .
sails. Three small squares are the windows.
Butterfly: two triangles are the wings. A circle and an oval make the body. Two small
black circles sit near the head.
Rocket: one triangle is the tip and one rectangle is the body. Two triangles are the fins.
Two small circles are the windows. A half circle is at the bottom.
Why Big pictures can be built out of a few simple shapes
: .
Let us Do — Page 46
Page 6 of 100
Page 8
l h h e i h h e A aS m · NCERT So ut ons
Boxes and an envelope
L E T US D O
Q1 Collect some cardboard boxes and open them up carefully. What shapes do you see in
the flattened boxes ?
You see rectangles (and sometimes squares).
box
A cardboard box cut open and pressed flat .
A box opens out into 6 flat faces Each face is a rectangle or a square
. .
− Exp anat on
l i
Why A box is a cuboid Each flat face of a cuboid is a rectangle and
: . ,
sometimes a square. Opposite faces are the same size, so the 6 faces come in
3 matching pairs.
Page 7 of 100
Boxes and an envelope
L E T US D O
Q1 Collect some cardboard boxes and open them up carefully. What shapes do you see in
the flattened boxes ?
You see rectangles (and sometimes squares).
box
A cardboard box cut open and pressed flat .
A box opens out into 6 flat faces Each face is a rectangle or a square
. .
− Exp anat on
l i
Why A box is a cuboid Each flat face of a cuboid is a rectangle and
: . ,
sometimes a square. Opposite faces are the same size, so the 6 faces come in
3 matching pairs.
Page 7 of 100
Page 9
l h h e i h h e A aS m · NCERT So ut ons
Q2 Make an Envelope Use a square piece of paper and fold it as shown in the picture
. .
1 2 3 4
The four folding steps printed in the book, from a square sheet to an envelope.
Fold a square sheet in four steps .
Keep the square standing on a corner.
Fold the left and right corners in.
Fold the bottom corner up.
Fold the top corner down to close it.
C heck i t yourself: Open the envelope again. The fold lines make triangles.
Baking biscuits — Page 47
Page 8 of 100
Q2 Make an Envelope Use a square piece of paper and fold it as shown in the picture
. .
1 2 3 4
The four folding steps printed in the book, from a square sheet to an envelope.
Fold a square sheet in four steps .
Keep the square standing on a corner.
Fold the left and right corners in.
Fold the bottom corner up.
Fold the top corner down to close it.
C heck i t yourself: Open the envelope again. The fold lines make triangles.
Baking biscuits — Page 47
Page 8 of 100
Page 10
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
Faces of boxes
co m
e m.
Observ.ceotmhe faces of these objects What is common among themglas
Q1
e m a
. ?
s
a gla
co m
e m . ag
g l as
a
. com
chocoelam
a s
com
TV screen box lid te bar
m . agl
ase
A TV screen a box lid and a bar of chocolate
agl
, .
m a s
.co agl
All of them have rectangular faces sem
a
agalnd the bar of chocolate are all rectangles
.
The TV screen the lid of the box
, .
Why Each face has sides and square corners like the biscuits .tchoatmfit so well in
m
:
se
4 4 ,
com a
the tray.
. a g l
m
ase
agl
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
com
m .
m ase
.co
a g l Page 9 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
Faces of boxes
co m
e m.
Observ.ceotmhe faces of these objects What is common among themglas
Q1
e m a
. ?
s
a gla
co m
e m . ag
g l as
a
. com
chocoelam
a s
com
TV screen box lid te bar
m . agl
ase
A TV screen a box lid and a bar of chocolate
agl
, .
m a s
.co agl
All of them have rectangular faces sem
a
agalnd the bar of chocolate are all rectangles
.
The TV screen the lid of the box
, .
Why Each face has sides and square corners like the biscuits .tchoatmfit so well in
m
:
se
4 4 ,
com a
the tray.
. a g l
m
ase
agl
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
com
m .
m ase
.co
a g l Page 9 of 100
Page 11
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Q2 Why did the two children get different shapes Discuss ? .
wooden box traced matchbox traced
The outlines the two children drew on their sheets.
Because they traced different faces .
The wooden box has a square face and a rectangle face. So one child got a square and a
rectangle.
The matchbox has three faces of different sizes. So the other child got three different
rectangles.
− Exp anat on
l i
Why The outline you draw is the shape of the face you place on the paper
: .
Q3 Name any three objects that have rectangular faces . _________________, ________________,
____________________
Any three of these are correct :
a maths book
a duster
a brick
Page 10 of 100
gl e l i
Q2 Why did the two children get different shapes Discuss ? .
wooden box traced matchbox traced
The outlines the two children drew on their sheets.
Because they traced different faces .
The wooden box has a square face and a rectangle face. So one child got a square and a
rectangle.
The matchbox has three faces of different sizes. So the other child got three different
rectangles.
− Exp anat on
l i
Why The outline you draw is the shape of the face you place on the paper
: .
Q3 Name any three objects that have rectangular faces . _________________, ________________,
____________________
Any three of these are correct :
a maths book
a duster
a brick
Page 10 of 100
Page 12
l h h e i h h e A aS m · NCERT So ut ons
a soap box, a matchbox, a mobile phone, a door
Tip: Place the object on paper and draw around it. If you get a rectangle, the face is
rectangular.
Let us Do — Page 48
Tracing the faces of a cuboid
L E T US D O
Q1 Trace all the faces of any cuboidal object example sharpener or eraser
.( — )
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
Take an eraser and trace every face.
Put the eraser on the page and draw around it.
Turn it on to the next face and draw again.
Do this for every face.
You get 6 outlines.
Page 11 of 100
a soap box, a matchbox, a mobile phone, a door
Tip: Place the object on paper and draw around it. If you get a rectangle, the face is
rectangular.
Let us Do — Page 48
Tracing the faces of a cuboid
L E T US D O
Q1 Trace all the faces of any cuboidal object example sharpener or eraser
.( — )
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
Take an eraser and trace every face.
Put the eraser on the page and draw around it.
Turn it on to the next face and draw again.
Do this for every face.
You get 6 outlines.
Page 11 of 100
Page 13
l h h e i h h e A aS m · NCERT So ut ons
− Exp anat on
l i
Why A cuboid has six flat faces so it can be traced six times
: , .
Q2 a How many different faces did you get
( ) ? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
You get 6 faces in all.
But only 3 of them are of different sizes The faces come in pairs The top matches the bottom
. . ,
the front matches the back, and one side matches the other side.
Why Opposite faces of a cuboid are always the same size
: .
Page 12 of 100
− Exp anat on
l i
Why A cuboid has six flat faces so it can be traced six times
: , .
Q2 a How many different faces did you get
( ) ? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
You get 6 faces in all.
But only 3 of them are of different sizes The faces come in pairs The top matches the bottom
. . ,
the front matches the back, and one side matches the other side.
Why Opposite faces of a cuboid are always the same size
: .
Page 12 of 100
Page 14
l h h e i h h e A aS m · NCERT So ut ons
Q3 ( b) What shapes are these faces ? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
They are rectangles.
If the object is a cube like a dice then every face is a square
, , .
Tip: A square is a special rectangle. All its four sides are equal.
Page 13 of 100
Q3 ( b) What shapes are these faces ? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
They are rectangles.
If the object is a cube like a dice then every face is a square
, , .
Tip: A square is a special rectangle. All its four sides are equal.
Page 13 of 100
Page 15
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
Q4 c Did you get a square
e
( ) ? __________________
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
an eraser (a cuboid) s
m a
m .co agl
An eraasseer It is a cuboid so it has six flat faces
agl
. , .
co m
m .
It depenodm as e
.c
s on the object you chose
a g l
m
.
a se An eraser usually gives only rectangles Then write No
agl
. .
A sharpener or a dice gives squares Then write Yes . .
se m
com g l a
. a
− Exp anat on
m
l i
ase
Why A face is a squaargelonly when all its four sides are equal in length
: .
co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 14 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
Q4 c Did you get a square
e
( ) ? __________________
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
an eraser (a cuboid) s
m a
m .co agl
An eraasseer It is a cuboid so it has six flat faces
agl
. , .
co m
m .
It depenodm as e
.c
s on the object you chose
a g l
m
.
a se An eraser usually gives only rectangles Then write No
agl
. .
A sharpener or a dice gives squares Then write Yes . .
se m
com g l a
. a
− Exp anat on
m
l i
ase
Why A face is a squaargelonly when all its four sides are equal in length
: .
co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 14 of 100
Page 16
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Q5 ( a a a a
d) C n you get six different rect ngles by tr cing cuboid? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
No.
Opposite faces of a cuboid are exactly the same. So the six outlines make only 3 different
rectangles, each drawn twice.
Why A cuboid has three pairs of matching faces not six different ones
: , .
Page 15 of 100
gl e l i
Q5 ( a a a a
d) C n you get six different rect ngles by tr cing cuboid? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
No.
Opposite faces of a cuboid are exactly the same. So the six outlines make only 3 different
rectangles, each drawn twice.
Why A cuboid has three pairs of matching faces not six different ones
: , .
Page 15 of 100
Page 17
l h h e i h h e A aS m · NCERT So ut ons
Q6 a a a aa
e C n cuboid h ve f ce like
( ) a triangle
? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
No.
Every face of a cuboid has sides and square corners A triangle has only sides
4 4 . 3 .
C heck i t yourself: Trace all six faces of your eraser. You will never get a triangle.
Page 16 of 100
Q6 a a a aa
e C n cuboid h ve f ce like
( ) a triangle
? __________________
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
No.
Every face of a cuboid has sides and square corners A triangle has only sides
4 4 . 3 .
C heck i t yourself: Trace all six faces of your eraser. You will never get a triangle.
Page 16 of 100
Page 18
l h h e i h h e A aS m · NCERT So ut ons
Q7 f
( ) The faces of a cuboid are __________________ or __________________ a
in sh pe.
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
The faces of a cuboid are rectangular or square in shape.
Why Each face has four sides and four square corners so it is a rectangle When
: , .
all four sides are equal, that rectangle is a square.
Let us Do — Page 49
Page 17 of 100
Q7 f
( ) The faces of a cuboid are __________________ or __________________ a
in sh pe.
an eraser (a cuboid)
An eraser It is a cuboid so it has six flat faces
. , .
The faces of a cuboid are rectangular or square in shape.
Why Each face has four sides and four square corners so it is a rectangle When
: , .
all four sides are equal, that rectangle is a square.
Let us Do — Page 49
Page 17 of 100
Page 19
l h h e i h h e A aS m · NCERT So ut ons
Making rectangles on a dot grid
L E T US D O
Q1 Construct the rectangles using the sides given below:
Four sets of sides already drawn on the dot grid
.
Add the missing sides to each drawing .
Count the dots along the side that is drawn.
Draw a side of the same length opposite it.
Join the ends.
Page 18 of 100
Making rectangles on a dot grid
L E T US D O
Q1 Construct the rectangles using the sides given below:
Four sets of sides already drawn on the dot grid
.
Add the missing sides to each drawing .
Count the dots along the side that is drawn.
Draw a side of the same length opposite it.
Join the ends.
Page 18 of 100
Page 20
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
e m.
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m .
The red dashed lines complete each rectangle.
a
ase
− Exp anat on
l i
agl
. c om
Why In a rectangle the opposite sides are equal so the mseissming side is always
m glathat is not given as
: ,
m .coas long as the one facing it Any length works for a saide
. ,
l a se long as the corners are square corners.
ag
.c
s e m
m a
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 19 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
e m.
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m .
The red dashed lines complete each rectangle.
a
ase
− Exp anat on
l i
agl
. c om
Why In a rectangle the opposite sides are equal so the mseissming side is always
m glathat is not given as
: ,
m .coas long as the one facing it Any length works for a saide
. ,
l a se long as the corners are square corners.
ag
.c
s e m
m a
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 19 of 100
Page 21
l h h e i h h e A aS m · NCERT So ut ons
Q2 Draw 3 bigger rectangles around the given rectangle.
One rectangle drawn on a grid of dots.
Draw each new rectangle one dot further out on every side .
Page 20 of 100
Q2 Draw 3 bigger rectangles around the given rectangle.
One rectangle drawn on a grid of dots.
Draw each new rectangle one dot further out on every side .
Page 20 of 100
Page 22
l h h e i h h e A aS m · NCERT So ut ons
Three bigger rectangles drawn around the given one.
− Exp anat on
l i
Start one dot out from the small rectangle and join four dots.
Go one more dot out and draw the next rectangle.
Go one more dot out again for the third one.
Why Moving out by the same number of dots on all sides keeps the corners
:
square.
Let us Do — Page 50
Page 21 of 100
Three bigger rectangles drawn around the given one.
− Exp anat on
l i
Start one dot out from the small rectangle and join four dots.
Go one more dot out and draw the next rectangle.
Go one more dot out again for the third one.
Why Moving out by the same number of dots on all sides keeps the corners
:
square.
Let us Do — Page 50
Page 21 of 100
Page 23
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Counting rectangles and looking at them
L E T US D O
Q1 Count and write the number of rectangles in the following picture. __________________
A big rectangle with lines drawn inside it .
There are 10 rectangles.
Page 22 of 100
gl e l i
Counting rectangles and looking at them
L E T US D O
Q1 Count and write the number of rectangles in the following picture. __________________
A big rectangle with lines drawn inside it .
There are 10 rectangles.
Page 22 of 100
Page 24
l h h e i h h e A aS m · NCERT So ut ons
4
1
3
5
2
The five small rectangles, numbered 1 to 5.
5 small ones
+ (1, 2) + (4, 5)
+ (1, 2, 3) + (3, 4, 5)
+ the whole picture
= 5 + 2 + 2 + 1 = 10
− Exp anat on
l i
Why Two or three small rectangles side by side can make a bigger rectangle
: ,
so they must be counted as well. 1 and 2 together fill the left strip; 4 and 5 fill
the right strip.
Page 23 of 100
4
1
3
5
2
The five small rectangles, numbered 1 to 5.
5 small ones
+ (1, 2) + (4, 5)
+ (1, 2, 3) + (3, 4, 5)
+ the whole picture
= 5 + 2 + 2 + 1 = 10
− Exp anat on
l i
Why Two or three small rectangles side by side can make a bigger rectangle
: ,
so they must be counted as well. 1 and 2 together fill the left strip; 4 and 5 fill
the right strip.
Page 23 of 100
Page 25
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
Q2 a How many sides are there in a rectangle
e
( ) ? ______________
com g l as
. a
a s em
ag l
com
e m . ag
g l as
a
co m
e m.
m l as
m .co a g
l a se
a g
mrent sizes lying at different angles a s
.co agl
Eleven rectangles of diffe , .
se m
g l a
a
co m
.
A rectangle has 4 sides
m
.
m as e
l
Pick any rectangle in the picture and run your finger round it. You touch four straight sides and
m .co
come back to the start. a g
l a se
ag Why Every rectangle is closed by four straight lines however big or small it is
: , .
se m
com g l a
m . a
ase
agl
co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 24 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
Q2 a How many sides are there in a rectangle
e
( ) ? ______________
com g l as
. a
a s em
ag l
com
e m . ag
g l as
a
co m
e m.
m l as
m .co a g
l a se
a g
mrent sizes lying at different angles a s
.co agl
Eleven rectangles of diffe , .
se m
g l a
a
co m
.
A rectangle has 4 sides
m
.
m as e
l
Pick any rectangle in the picture and run your finger round it. You touch four straight sides and
m .co
come back to the start. a g
l a se
ag Why Every rectangle is closed by four straight lines however big or small it is
: , .
se m
com g l a
m . a
ase
agl
co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 24 of 100
Page 26
l h h e i h h e A aS m · NCERT So ut ons
Q3 ( a
b) How m ny corners are there in a rectangle ? ______________
Eleven rectangles of different sizes lying at different angles
, .
A rectangle has 4 corners .
A corner is made where two sides meet Four sides meet at four places
. .
Tip: A rectangle always has as many corners as sides.
Page 25 of 100
Q3 ( a
b) How m ny corners are there in a rectangle ? ______________
Eleven rectangles of different sizes lying at different angles
, .
A rectangle has 4 corners .
A corner is made where two sides meet Four sides meet at four places
. .
Tip: A rectangle always has as many corners as sides.
Page 25 of 100
Page 27
l h h e i h h e A aS m · NCERT So ut ons
Q4 c Are there
( ) any sides in a rectangle that are equal in length to each other ?
______________
Eleven rectangles of different sizes lying at different angles
, .
Yes.
The two sides facing each other are equal. So a rectangle has two pairs of equal sides.
C t yourself: Measure the long sides of this page with a thread. They are the
heck i
same length.
Page 26 of 100
Q4 c Are there
( ) any sides in a rectangle that are equal in length to each other ?
______________
Eleven rectangles of different sizes lying at different angles
, .
Yes.
The two sides facing each other are equal. So a rectangle has two pairs of equal sides.
C t yourself: Measure the long sides of this page with a thread. They are the
heck i
same length.
Page 26 of 100
Page 28
l h h e i h h e A aS m · NCERT So ut ons
Q5 d)
( What do you notice in a rectangle Describe it in your own words
? .
_______________________________________________________
Eleven rectangles of different sizes lying at different angles
, .
Sample answer:
A rectangle has straight sides and corners
4 4 .
The sides facing each other are equal.
All its corners are square corners.
It can be big or small, lying down or standing up.
− Exp anat on
l i
Why Turning a rectangle does not change its sides or its corners so it is still a
: ,
rectangle.
Same to Same — Page 51
Page 27 of 100
Q5 d)
( What do you notice in a rectangle Describe it in your own words
? .
_______________________________________________________
Eleven rectangles of different sizes lying at different angles
, .
Sample answer:
A rectangle has straight sides and corners
4 4 .
The sides facing each other are equal.
All its corners are square corners.
It can be big or small, lying down or standing up.
− Exp anat on
l i
Why Turning a rectangle does not change its sides or its corners so it is still a
: ,
rectangle.
Same to Same — Page 51
Page 27 of 100
Page 29
l h h e i h h e A aS m · NCERT So ut ons
A square and a rectangle
Q1 I wonder what is the difference between a square and a rectangle?
square rectangle
A square and a rectangle side by side
, .
The difference is in the sides.
In a square all four sides are equal
, .
In a rectangle only the opposite sides need to be equal
, .
− Exp anat on
l i
Why A square follows a stricter rule so every square is also a rectangle But a
: , .
rectangle need not be a square.
Page 28 of 100
A square and a rectangle
Q1 I wonder what is the difference between a square and a rectangle?
square rectangle
A square and a rectangle side by side
, .
The difference is in the sides.
In a square all four sides are equal
, .
In a rectangle only the opposite sides need to be equal
, .
− Exp anat on
l i
Why A square follows a stricter rule so every square is also a rectangle But a
: , .
rectangle need not be a square.
Page 28 of 100
Page 30
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
Q2 Both have sides
e
1. _________ .
m l as
m.co a g
l a se
a g
com
e m . ag
g l as
a
co m
m.
m ase
agl
square rectangle
m .co
l a se A square and a rectangle side by side
a g
, .
m a s
em
.co agl
Both have 4 sides g l as
a
.
Count the sides of the square Count the sides of the rectangle
: 1, 2, 3, 4. : 1, 2, 3, 4.
os m
Why A square is a special rectangle so it has the same numbeer mof.scide
m a s
: , .
m.co agl
l a se
ag
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 29 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
m.
Q2 Both have sides
e
1. _________ .
m l as
m.co a g
l a se
a g
com
e m . ag
g l as
a
co m
m.
m ase
agl
square rectangle
m .co
l a se A square and a rectangle side by side
a g
, .
m a s
em
.co agl
Both have 4 sides g l as
a
.
Count the sides of the square Count the sides of the rectangle
: 1, 2, 3, 4. : 1, 2, 3, 4.
os m
Why A square is a special rectangle so it has the same numbeer mof.scide
m a s
: , .
m.co agl
l a se
ag
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 29 of 100
Page 31
l h h e i h h e A aS m · NCERT So ut ons
Q3 2. Both have _________ corners.
square rectangle
A square and a rectangle side by side
, .
Both have 4 corners .
All eight of these corners are square corners .
Tip: Put the corner of your maths book on each corner. It fits every time.
Page 30 of 100
Q3 2. Both have _________ corners.
square rectangle
A square and a rectangle side by side
, .
Both have 4 corners .
All eight of these corners are square corners .
Tip: Put the corner of your maths book on each corner. It fits every time.
Page 30 of 100
Page 32
l h h e i h h e A aS m · NCERT So ut ons
Q4 How many squares do you see in this drawing?
A square with more lines drawn inside it .
There are 6 squares.
Page 31 of 100
Q4 How many squares do you see in this drawing?
A square with more lines drawn inside it .
There are 6 squares.
Page 31 of 100
Page 33
l h h e i h h e A aS m · NCERT So ut ons
1
2
3
The three small squares are numbered. The dashed lines show two middle-sized squares; the
outside edge is the sixth square.
3 small squares
+ 2 middle-sized squares
+ 1 big square
=6
Page 32 of 100
1
2
3
The three small squares are numbered. The dashed lines show two middle-sized squares; the
outside edge is the sixth square.
3 small squares
+ 2 middle-sized squares
+ 1 big square
=6
Page 32 of 100
Page 34
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
− Exp anat on
l i
Why Some squares are hidden inside bigger ones The two dashed middle
: . -
sized squares each hold one small square and an L-shaped piece. So look for
small, middle and big sizes.
Let us Do — Page 52–53 s
Making squares
L E T US D O
Q1 Here is a square. Draw 2 bigger squares around this square.
A square drawn on a grid of dots .
Draw each new square one dot further out on every side .
Page 33 of 100
gl e l i
− Exp anat on
l i
Why Some squares are hidden inside bigger ones The two dashed middle
: . -
sized squares each hold one small square and an L-shaped piece. So look for
small, middle and big sizes.
Let us Do — Page 52–53 s
Making squares
L E T US D O
Q1 Here is a square. Draw 2 bigger squares around this square.
A square drawn on a grid of dots .
Draw each new square one dot further out on every side .
Page 33 of 100
Page 35
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
e m.
m l as
m .co a g
l a se
ag
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
Two bigger squares drawn around the given square.
m .
m as e
.co a g l
se −mExp anat on
g l a
l i
a
m
Move one dot out on the left, right, top and bottom. Join those four dots.
Move one more dot out and join four m
l a se
co g
dots again.
m . a
Why Moving out by theglasasme e number of dots on all four sides keeps all the
sides equal so the shaape stays a square
:
, .
co m
m .
o m l a se
.c a g
m
se Q2 Use matchsticks to make a square so that it has squares on all its sides How many
l a
ag
.
squares did you get
.c
?
s e m
m a
e m . co agl
You get 5 squares.
g l as
a
co m
m .
m ase
.co
a g l Page 34 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
e m.
m l as
m .co a g
l a se
ag
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
Two bigger squares drawn around the given square.
m .
m as e
.co a g l
se −mExp anat on
g l a
l i
a
m
Move one dot out on the left, right, top and bottom. Join those four dots.
Move one more dot out and join four m
l a se
co g
dots again.
m . a
Why Moving out by theglasasme e number of dots on all four sides keeps all the
sides equal so the shaape stays a square
:
, .
co m
m .
o m l a se
.c a g
m
se Q2 Use matchsticks to make a square so that it has squares on all its sides How many
l a
ag
.
squares did you get
.c
?
s e m
m a
e m . co agl
You get 5 squares.
g l as
a
co m
m .
m ase
.co
a g l Page 34 of 100
Page 36
l h h e i h h e A aS m · NCERT So ut ons
1 square in the middle + 4 squares around it = 5
− Exp anat on
l i
Make one square with 4 matchsticks in the middle.
Build one more square on each of its four sides.
Each new square shares one side with the middle square so it needs only new
, 3
matchsticks.
4 + 3 + 3 + 3 + 3 = 16 matchsticks
Page 35 of 100
1 square in the middle + 4 squares around it = 5
− Exp anat on
l i
Make one square with 4 matchsticks in the middle.
Build one more square on each of its four sides.
Each new square shares one side with the middle square so it needs only new
, 3
matchsticks.
4 + 3 + 3 + 3 + 3 = 16 matchsticks
Page 35 of 100
Page 37
l h h e i h h e A aS m · NCERT So ut ons
Q3 Complete the squares using the sides given below.
Four sets of sides already drawn on the dot grid
.
Every side of a square must be the same length .
Count the dots along the side that is drawn.
Draw the other sides just as long.
Join the ends.
Page 36 of 100
Q3 Complete the squares using the sides given below.
Four sets of sides already drawn on the dot grid
.
Every side of a square must be the same length .
Count the dots along the side that is drawn.
Draw the other sides just as long.
Join the ends.
Page 36 of 100
Page 38
l h h e i h h e A aS m · NCERT So ut ons
The red dashed lines complete each square.
− Exp anat on
l i
Why All four sides of a square are equal so one given side tells you the length
: ,
of the rest.
Page 37 of 100
The red dashed lines complete each square.
− Exp anat on
l i
Why All four sides of a square are equal so one given side tells you the length
: ,
of the rest.
Page 37 of 100
Page 39
l h h e i h h e A aS m · NCERT So ut ons
Q4 Use the square cutouts from the book to do this activity How many different shapes
.
can you make by joining a squares Show them on a dot grid
( ) 2 ? .
A small grid of dots to draw on .
Only 1 shape.
Page 38 of 100
Q4 Use the square cutouts from the book to do this activity How many different shapes
.
can you make by joining a squares Show them on a dot grid
( ) 2 ? .
A small grid of dots to draw on .
Only 1 shape.
Page 38 of 100
Page 40
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
e m.
m l as
m .co a g
l a se
a g
co m
m . ag
l a se
ag
the same shape, just turned
co m
Two squares joined edge to edge shown lying down and stanadisneg up
m.
m
.c o agl
, .
a s em
a gTlwo squares joined along a side make a rectangle Standing it up does not make a new shape
. .
m a s
.co agl
− Exp anat on
l i
a s em
Why Turning a shape daoegsl not make it a new shape
: .
co m
m .
m ase
.co a g l
se m
g l a
a
se m
com g l a
m. a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 39 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
co m
e m.
m l as
m .co a g
l a se
a g
co m
m . ag
l a se
ag
the same shape, just turned
co m
Two squares joined edge to edge shown lying down and stanadisneg up
m.
m
.c o agl
, .
a s em
a gTlwo squares joined along a side make a rectangle Standing it up does not make a new shape
. .
m a s
.co agl
− Exp anat on
l i
a s em
Why Turning a shape daoegsl not make it a new shape
: .
co m
m .
m ase
.co a g l
se m
g l a
a
se m
com g l a
m. a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 39 of 100
Page 41
l h h e i h h e A aS m · NCERT So ut ons
Q5 How many different shapes can you make by joining (b) 3 squares
A small grid of dots to draw on .
You can make 2 different shapes.
Page 40 of 100
Q5 How many different shapes can you make by joining (b) 3 squares
A small grid of dots to draw on .
You can make 2 different shapes.
Page 40 of 100
Page 42
l h h e i h h e A aS m · NCERT So ut ons
a straight one an L-shaped one
The two shapes you can make with three squares.
All three squares in a straight line .
Two in a line and the third turning the corner, like the letter L.
− Exp anat on
l i
Tip: Show them on a dot grid so the squares stay the same size.
Page 41 of 100
a straight one an L-shaped one
The two shapes you can make with three squares.
All three squares in a straight line .
Two in a line and the third turning the corner, like the letter L.
− Exp anat on
l i
Tip: Show them on a dot grid so the squares stay the same size.
Page 41 of 100
Page 43
l h h e i h h e A aS m · NCERT So ut ons
Q6 How many different shapes can you make by joining (c) 4 squares
A small grid of dots to draw on .
You can make 5 different shapes.
Page 42 of 100
Q6 How many different shapes can you make by joining (c) 4 squares
A small grid of dots to draw on .
You can make 5 different shapes.
Page 42 of 100
Page 44
l h h e i h h e A aS m · NCERT So ut ons
five different shapes in all
The five shapes you can make by joining four squares.
A straight line of four a big square an L a T and a step shape
, , , .
− Exp anat on
l i
Why Two shapes count as one if you can turn or flip your paper to make them
:
match.
Let us Explore — Page 53
Page 43 of 100
five different shapes in all
The five shapes you can make by joining four squares.
A straight line of four a big square an L a T and a step shape
, , , .
− Exp anat on
l i
Why Two shapes count as one if you can turn or flip your paper to make them
:
match.
Let us Explore — Page 53
Page 43 of 100
Page 45
ase
l h h e i h h e
a g l A aS m · NCERT So ut ons
Which shapes are rectangles?
co m
se m.
m a
L E T US E XPLOR E
.c o a g l
e m
Q1 laTsick ✓ the shapes that are rectangles Which figures are not rectangles Explain why
ag
. ? .
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
em
.co agl
A bolaardswith eleven paper shapes pinned on it
ag
.
co m
m .
e
5 shapceosm g l as
m . are rectangles tick them The other 6 are not
a
ase
( ). .
agl
se m
s e m .com ✓ ag l a
a
agl
✓ em . co m
as
m .co
m ✓ a g l
ase ✓
agl
m
✓ a s e m .c
m . co agl
l a se The five rectangles carry a tick.
ag
co m
m .
m ase
.co
a g l Page 44 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
Which shapes are rectangles?
co m
se m.
m a
L E T US E XPLOR E
.c o a g l
e m
Q1 laTsick ✓ the shapes that are rectangles Which figures are not rectangles Explain why
ag
. ? .
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
em
.co agl
A bolaardswith eleven paper shapes pinned on it
ag
.
co m
m .
e
5 shapceosm g l as
m . are rectangles tick them The other 6 are not
a
ase
( ). .
agl
se m
s e m .com ✓ ag l a
a
agl
✓ em . co m
as
m .co
m ✓ a g l
ase ✓
agl
m
✓ a s e m .c
m . co agl
l a se The five rectangles carry a tick.
ag
co m
m .
m ase
.co
a g l Page 44 of 100
Page 46
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
The 6 shapes that are not rectangles have sloping sides, so their corners are not square
corners.
− Exp anat on
l i
Why A shape is a rectangle only when it has sides
: 4 square corners, and
, 4
opposite sides equal. The blue square is a rectangle too. Check each corner
with the corner of your book: in the 6 other shapes it does not fit.
Q2 Can you fold all the corners of a square sheet in such a way that the number of corners
remains the same ?
Yes.
Fold all four corners in to the middle point The folded sheet is a smaller square It still has 4
. .
corners.
− Exp anat on
l i
Why Each fold line joins the middle points of two sides These four middle
: .
points become the new corners.
Page 45 of 100
gl e l i
The 6 shapes that are not rectangles have sloping sides, so their corners are not square
corners.
− Exp anat on
l i
Why A shape is a rectangle only when it has sides
: 4 square corners, and
, 4
opposite sides equal. The blue square is a rectangle too. Check each corner
with the corner of your book: in the 6 other shapes it does not fit.
Q2 Can you fold all the corners of a square sheet in such a way that the number of corners
remains the same ?
Yes.
Fold all four corners in to the middle point The folded sheet is a smaller square It still has 4
. .
corners.
− Exp anat on
l i
Why Each fold line joins the middle points of two sides These four middle
: .
points become the new corners.
Page 45 of 100
Page 47
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Q3 Make a square on a cardboard sheet and cut along the dotted lines marked on the
square as shown to get triangles Make as many different shapes as possible by
4 .
joining three triangles together How many shapes can you make Now try with four
. ? ,
triangles together .
A square with two dotted lines drawn corner to corner .
With three triangles you can make 4 different shapes.
Page 46 of 100
gl e l i
Q3 Make a square on a cardboard sheet and cut along the dotted lines marked on the
square as shown to get triangles Make as many different shapes as possible by
4 .
joining three triangles together How many shapes can you make Now try with four
. ? ,
triangles together .
A square with two dotted lines drawn corner to corner .
With three triangles you can make 4 different shapes.
Page 46 of 100
Page 48
l h h e i h h e A aS m · NCERT So ut ons
shape 1 shape 2
Two of the shapes you can build from three of the triangles.
With four triangles you can make many more 14. Draw each one you find.
− Exp anat on
l i
Cut the square along both dotted lines. You get 4 triangles.
Join three of them, always matching a full side to a full side.
Turn each new shape to check it is really new.
Why Two shapes are the same if you can turn or flip one on to the other
: .
Square Corners — Page 54
Page 47 of 100
shape 1 shape 2
Two of the shapes you can build from three of the triangles.
With four triangles you can make many more 14. Draw each one you find.
− Exp anat on
l i
Cut the square along both dotted lines. You get 4 triangles.
Join three of them, always matching a full side to a full side.
Turn each new shape to check it is really new.
Why Two shapes are the same if you can turn or flip one on to the other
: .
Square Corners — Page 54
Page 47 of 100
Page 49
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Corners of squares and rectangles
Q1 Which tile will fit in the corner of this table Will the same tile fit in the corner of the
?
math book ?
corner of the table square tile triangle tile
The corner of a table, a square tile and a triangle tile.
The square tile will fit.
Yes, the same tile fits the corner of the maths book too.
Why The table top and the book are both rectangles All their corners are square
: .
corners, and a square tile has square corners as well.
Page 48 of 100
gl e l i
Corners of squares and rectangles
Q1 Which tile will fit in the corner of this table Will the same tile fit in the corner of the
?
math book ?
corner of the table square tile triangle tile
The corner of a table, a square tile and a triangle tile.
The square tile will fit.
Yes, the same tile fits the corner of the maths book too.
Why The table top and the book are both rectangles All their corners are square
: .
corners, and a square tile has square corners as well.
Page 48 of 100
Page 50
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
Are the corners of a square the same? How do you know? Pile up some squ.caorems over
m
Q2
one another and see a se
com g l
.
. a
a s em
a gl
co m
e m . ag
g l as
a
co m
se m.
m l a
m .co square tagngle
reca
ase
agl A square and a rectangle side by side
, .
m a s
m .co agl
l a se
g
Yes all four corners of a squarae are the same
, .
Pile some same-size squares on one another. Every corner sits exactly on the corner below it.
com
m .
− Exp am as e
.co
nat on
l i
a g l
a s em
agl Why All four corners of a square are square corners so they match perfectly
: , .
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 49 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
Are the corners of a square the same? How do you know? Pile up some squ.caorems over
m
Q2
one another and see a se
com g l
.
. a
a s em
a gl
co m
e m . ag
g l as
a
co m
se m.
m l a
m .co square tagngle
reca
ase
agl A square and a rectangle side by side
, .
m a s
m .co agl
l a se
g
Yes all four corners of a squarae are the same
, .
Pile some same-size squares on one another. Every corner sits exactly on the corner below it.
com
m .
− Exp am as e
.co
nat on
l i
a g l
a s em
agl Why All four corners of a square are square corners so they match perfectly
: , .
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 49 of 100
Page 51
l h h e i h h e A aS m · NCERT So ut ons
Q3 Are the corners of a rectangle the same? How do you know? Pile up some rectangles
over one another and see .
square rectangle
A square and a rectangle side by side
, .
Yes all four corners of a rectangle are the same
, .
Pile some same-size rectangles on one another. The corners match exactly.
− Exp anat on
l i
C t yourself: Fold a paper rectangle in half and then in half again. All four
heck i
corners come together in one heap and match.
Page 50 of 100
Q3 Are the corners of a rectangle the same? How do you know? Pile up some rectangles
over one another and see .
square rectangle
A square and a rectangle side by side
, .
Yes all four corners of a rectangle are the same
, .
Pile some same-size rectangles on one another. The corners match exactly.
− Exp anat on
l i
C t yourself: Fold a paper rectangle in half and then in half again. All four
heck i
corners come together in one heap and match.
Page 50 of 100
Page 52
l h h e i h h e A aS m · NCERT So ut ons
Q4 Are the corners of the square and a rectangle the same?
square rectangle
A square and a rectangle side by side
, .
Yes, they are the same.
Put the corner of a square on the corner of a rectangle. They fit on top of each other.
Why Both shapes have square corners That is why such a corner is called a
: .
square corner.
Q5 Name some objects in your class that have only square corners . _____________________
Things in the class with only square corners:
the blackboard
the maths book and the notebook
the duster
the window, the door and the desk top
Tip: Hold the corner of your book against the object. If it fits, that is a square corner.
Page 51 of 100
Q4 Are the corners of the square and a rectangle the same?
square rectangle
A square and a rectangle side by side
, .
Yes, they are the same.
Put the corner of a square on the corner of a rectangle. They fit on top of each other.
Why Both shapes have square corners That is why such a corner is called a
: .
square corner.
Q5 Name some objects in your class that have only square corners . _____________________
Things in the class with only square corners:
the blackboard
the maths book and the notebook
the duster
the window, the door and the desk top
Tip: Hold the corner of your book against the object. If it fits, that is a square corner.
Page 51 of 100
Page 53
l h h e i h h e A aS m · NCERT So ut ons
Q6 Are the corners of this shape the same as that of a square and a rectangle?
square rectangle triangle
A square a rectangle and a triangle
, .
No. The corners of this triangle are not square corners .
Hold the corner of your book against each corner of the triangle It does not fit any of them
. .
Why Every corner of this triangle is less than a square corner
: .
Let us Do — Page 55
Page 52 of 100
Q6 Are the corners of this shape the same as that of a square and a rectangle?
square rectangle triangle
A square a rectangle and a triangle
, .
No. The corners of this triangle are not square corners .
Hold the corner of your book against each corner of the triangle It does not fit any of them
. .
Why Every corner of this triangle is less than a square corner
: .
Let us Do — Page 55
Page 52 of 100
Page 54
l h h e i h h e A aS m · NCERT So ut ons
gl e l i
Paper strips and square corners
L E T US D O
Q1 Use the strips to show a square corner more than a square corner and less than a
,
square corner .
less than a square corner square corner more than a square corner
Two paper strips joined at one end, opened by three different amounts.
Join two paper strips at one end, then open them.
Open like the corner of your book: square corner.
Open a little: less than a square corner.
Open wider: more than a square corner.
− Exp anat on
l i
Why The wider the strips open the bigger the corner becomes
: , .
Page 53 of 100
gl e l i
Paper strips and square corners
L E T US D O
Q1 Use the strips to show a square corner more than a square corner and less than a
,
square corner .
less than a square corner square corner more than a square corner
Two paper strips joined at one end, opened by three different amounts.
Join two paper strips at one end, then open them.
Open like the corner of your book: square corner.
Open a little: less than a square corner.
Open wider: more than a square corner.
− Exp anat on
l i
Why The wider the strips open the bigger the corner becomes
: , .
Page 53 of 100
Page 55
ase
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
Can you use the strip to check whether the corner of your table and the bo.acrodmare
m
Q2
square corners a se
com g l
?
. a
a s em
a gl
co m
em . ag
g l as
a
co m
m.
ss than a square corner square corner more than a square corner
se
le
m l a
.co ag rent amounts
sem
Two paper strips joined at one end opened by three diffe
, .
a
agl
m a s
.co agl
Yes.
a s em
Set the strips to a square cornergalnd hold them on the corner of the table If both strips lie
,
a
along the edges it is a square corner The table and the board have square corners
.
.
.
co m
− Exp anat on
m .
as e
l i
m l
.co a g
a s emT p The strips work like a small checking tool for corners
gl
i : .
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 54 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
gl e l i
Can you use the strip to check whether the corner of your table and the bo.acrodmare
m
Q2
square corners a se
com g l
?
. a
a s em
a gl
co m
em . ag
g l as
a
co m
m.
ss than a square corner square corner more than a square corner
se
le
m l a
.co ag rent amounts
sem
Two paper strips joined at one end opened by three diffe
, .
a
agl
m a s
.co agl
Yes.
a s em
Set the strips to a square cornergalnd hold them on the corner of the table If both strips lie
,
a
along the edges it is a square corner The table and the board have square corners
.
.
.
co m
− Exp anat on
m .
as e
l i
m l
.co a g
a s emT p The strips work like a small checking tool for corners
gl
i : .
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 54 of 100
Page 56
l h h e i h h e A aS m · NCERT So ut ons
Q3 Mark the square corners in these shapes .
Six shapes in a row.
Three shapes have square corners.
Red rings mark every square corner.
The green square: 4.
The blue square standing on its corner: 4.
The tall red rectangle: 4.
The other three shapes have none.
− Exp anat on
l i
Why Only squares and rectangles have all their corners square Check each
: .
corner with the corner of your book.
Page 55 of 100
Q3 Mark the square corners in these shapes .
Six shapes in a row.
Three shapes have square corners.
Red rings mark every square corner.
The green square: 4.
The blue square standing on its corner: 4.
The tall red rectangle: 4.
The other three shapes have none.
− Exp anat on
l i
Why Only squares and rectangles have all their corners square Check each
: .
corner with the corner of your book.
Page 55 of 100
Page 57
l h h e i h h e A aS m · NCERT So ut ons
Q4 Connect the dots to make some squares. How many different squares did you get?
_____________________
Eight dots set out in a ring .
You get 2 squares.
Page 56 of 100
Q4 Connect the dots to make some squares. How many different squares did you get?
_____________________
Eight dots set out in a ring .
You get 2 squares.
Page 56 of 100
Page 58
l h h e i h h e A aS m · NCERT So ut ons
Two squares of the same size, one standing straight and one turned.
Join every other dot. The top, bottom, left and right dots make one square. The other four dots
make the second square.
− Exp anat on
l i
Why The eight dots sit in a ring so every other dot makes one square There
: , .
are two such sets of four dots.
Let us Do — Page 56
Page 57 of 100
Two squares of the same size, one standing straight and one turned.
Join every other dot. The top, bottom, left and right dots make one square. The other four dots
make the second square.
− Exp anat on
l i
Why The eight dots sit in a ring so every other dot makes one square There
: , .
are two such sets of four dots.
Let us Do — Page 56
Page 57 of 100
Page 59
l h h e i h h e A aS m · NCERT So ut ons
The boat, and matchstick corners
L E T US D O
Q1 Look at the picture given below and answer the following a Count and write the
.( )
number of corners .
A boat built out of flat shapes .
The boat has 17 corners.
mast 4 + flag 3 + red sail 3 + blue sail 3 + boat 4
= 17
Page 58 of 100
The boat, and matchstick corners
L E T US D O
Q1 Look at the picture given below and answer the following a Count and write the
.( )
number of corners .
A boat built out of flat shapes .
The boat has 17 corners.
mast 4 + flag 3 + red sail 3 + blue sail 3 + boat 4
= 17
Page 58 of 100
Page 60
as e
l h h e i h h e
a g l A aS m · NCERT So ut ons
co m
m.
− Exp anat on
l i
o m l a se
c the corners of each piece one by one then add aTghe mast and the
WheymC.ount
baosat have corners each the flag and the two sails are triangles with corners
: , .
a g l 4 ; 3
each.
com
e m . ag
g l as
a
Q2 b Circle the square corners
m
( ) .
co
em.
m l as
m .co a g
l a se
a g
m a s
m.co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m A boat built out of flat shapes
g l a
.
a c
m .
m a s e
. co agl
e m
There are 6 square corners.
g l as
a
co m
m .
m as e
.co
a g l Page 59 of 100
l h h e i h h e
a g l A aS m · NCERT So ut ons
co m
m.
− Exp anat on
l i
o m l a se
c the corners of each piece one by one then add aTghe mast and the
WheymC.ount
baosat have corners each the flag and the two sails are triangles with corners
: , .
a g l 4 ; 3
each.
com
e m . ag
g l as
a
Q2 b Circle the square corners
m
( ) .
co
em.
m l as
m .co a g
l a se
a g
m a s
m.co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m A boat built out of flat shapes
g l a
.
a c
m .
m a s e
. co agl
e m
There are 6 square corners.
g l as
a
co m
m .
m as e
.co
a g l Page 59 of 100
Document Details
| Board / Org | NCERT |
| Exam | Class 3 |
| Type | Solution |
| Pages | 101 |
| Language | english |
| Updated | 13 Oct 2026 |