Class 7 Maths Notes for Perimeter And Area

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CLASS 7
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PERIMETER AND AREA

I. Important concepts/Result.
1. Perimeter of a polygon is the sum of length of all sides.
2. Perimeter of a regular polygon
= number of sides× length of one side.
Perimeter of square = 4 × side = 4 L
Perimeter of a rectangle = 2 (l + b)
Circumference is the perimeter of a circle = 2 π r
22
Where π = 7 or 3.14
3.Area of a polygon is the space occupied by the figure in a plane.
Area of square = side × side
Area of rectangle = length × breadth
Area of parallelogram = base × height
1
Area of triangle = 2 base × height
Area of a circle = π r2

II. Some illustrations/Examples.
(i) MCQ
1. The area of a parallelogram of height 4 cm and base 6cm
(a) 4cm2 (b) 6cm2 (c) 12cm2 (d)
Answer: d
2. The area of a triangle of height 4cm and base 6cm.
(a) 4cm2 (b) 6cm2 (c) 12cm2 (d) 24cm2
Answer: C
3. The circumference of a circle of radius 7cm is.
(a) 7cm (b) 22cm (c) 44cm (d) 28cm
Answer: C
4. The area of a circle of radius 14cm is.
(a) 4312cm2 (b) 616cm2 (c) 308cm2 (d) 2156cm2
Answer:b

(ii)Case Study-1

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Mohan is the head (mukhiya) of his village and also a social worker. In his village there is no
school building so he plans to construct a school in his village. The length and breadth of the
school plot are in the ratio 10:3. The perimeter of the school plot is 260m. He also gives a
square plot for playground near the school. The area of square plot is same as the length of the
school plot.
(a) Form a linear equation for the perimeter of school plot
(a) 13x = 260 (b) 100x = 260 (c) 26x = 260 (d) 20x = 260
(b) Find the length of school plot
(a) 10m (b) 20m (c) 30m (d) 100m
(c) Find area of rectangular plot
(a) 100m2 (b) 300m2 (c) 3000m2 (d) 260m2
Solution:
(a) p = 260m
let length = 10x & breadth = 3x
2x (10x + 3x) = 260
26x = 260
(b) x = 10
Length = 10 ×10 = 100m
(c) Breadth = 3×10 = 30m
Area of rectangular plot = 100×30m2
= 3000m2
(iii) Short answer type question
1. Find the height of the parallelogram whose base is 10cm area is 80cm2
Solution: Area = base × height
80cm2= 10 cm × h
h = 8cm
2. Find the base length of a triangle whose area is 64cm2and height is 8cm.
1
Solution: Area of triangle = 2 b × h
1
64cm2= 2 × b × 8cm
b = 16cm.
3. What is the circumference of a circle of area 154 cm2
Solution: Area = π r2= 154cm2
22
× r2= 154cm2
7
154×7cm 2
r2 = = 49cm2
22
r= 7cm
22
Circumference = 2 π r= 2 × 7 ×7cm = 44cm
(iv) Long answer type question

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1. In an isosceles triangle ABC, with AB = AC = 10cm and BC= 12cm, the height AD from A to
BC is 8cm. Find the area of ∆ABC. What Will be the height from C to AB.
1
Solution: area ∆ABC = 2 b × h
1
=2 × BC×AD
1
=2 × 12cm × 8cm = 48cm2
1 1
Also, area ∆ABC = 2bh= 2 AB × CE
1
48cm2= 2 ×10cm × CE
48 cm 2 × 2
= CE
10 CM

CE = 9.6cm
2. How many times a wheel of radius 14 cm must rotate to go 88m.
Solution: let no. of rotations = n
n × distance covered in one rotation = total distance covered
n × 2 π r = 88m
22
n × 2 × 7 × 14m = 88 ×100cm
88×100×7cm
n = 2×22×14cm
n = 100
Required number of rotations = 100
III. Question for practice
(A) MCQ
1. Find the area of a parallelogram of base 10cm and height 8cm.
(a) 10cm2 (b) 8cm2 (c) 80cm2 (d) 160cm2
2. Find the area of a triangle of base 10cm and height 8cm.
(a) 10cm2 (b) 8cm2 (c) 40cm2 (d) 80cm2
3. Find the circumference of a circle of radius 3.5cm.
(a) 7cm (b) 22cm (c) 44cm (d) 88cm
4. Find the circumference of a circle of diameter 7cm.
(a) 7cm (b) 22cm (c) 44cm (d) 88cm
2
5. Find the area of a circle (in cm ) whose radius is 10cm. (π=3.14)
(a) 3.14 (b) 31.4 (c) 314 (d) 3140
2
6. Find the length of base of a triangle whose area is 100cm and altitude is 10cm.
(a) 20cm (b) 15cm (c) 10cm (d) 5cm
7. Find the area of a circle (in cm2) whose diameter is 20cm.
(a) 3.14 (b) 31.4 (c) 314 (d) 3140
8. Find the area of a parallelogram of height 5cm and base length 8cm.
(a) 40cm2 (b) 20cm2 (c) 10cm2 (d) 8cm2

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9. Find the area of a right triangle whose length of perpendicular sides are 8cm and 6sm
respectively.
(a) 64cm2 (b) 48cm2 (c) 24cm2 (d) 12cm2
10. Find the length of base of a parallelogram whose altitude is 11cm and area is 132cm2.
(a) 11cm (b) 12cm (c) 13cm (d) 14cm

(B) Short answer type question
1. The Area of a rectangle and area of a circle are equal. If the dimension of the rectangle are
14cm × 11cm, then find the radius of the circle.
2. A wire is bent to form a square of side 22cm. If the wire is rebent to form a circle, find its
radius.
3. What will be the diameter and area of a circle whose circumference is 88cm.
4. A wire is in the form of a rectangle of length 14cm and breadth 11cm. If the wire is rebent to
form a circle, find its radius.
5. Find area of a triangle of base 6cm and height 3.5cm.
6. Find the area of a parallelogram of base 10cm and altitude 7.5 cm.
7. Find the height of the parallelogram of area 14.5cm2 and base 5.8cm.
8. A wire is in the form of a parallelogram with side length 8cm and 6cm. If it is rebent into a
square, what will be length of the square
9. Which encloses more area, a triangle of height 10cm & base 8cm or a parallelogram of height
10cm & base 8cm.
10. What is the perimeter of a semicircular disc of diameter 7cm.

(C) Long answer type question
1. Find the cost of polishing a circular table top of diameter 20m. If the rate of polishing is ₹ 12
per m2.
2. From a circular card board sheet of radius 21cm, two circles of radius 3-5cm and a rectangle
of dimension 2cm×1cm are removed. Find the remaining area.
3. What is the area swept by a minute hand 7cm long, of a clock, in 30 minutes.
4. A farmer wants to fence his circular farm land of diameter 28m. Find the length of wire
required, if he makes 3 rounds of the fence. Also find the cost of wire at the rate of ₹12 per m.
5. ABCD is a parallelogram with base AB = 20cm and corresponding altitude DL = 15cm. If BC
= 25cm then find the altitude BM where BM is perpendicular to AD.
6. ∆ABC is right angled at B. With sides AB = 6m, BC = 8 m, and CA = 10m. Find the area of
∆ABC. Also find the length of altitude BD where BD is perpendicular to AC

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Case Study based Question

1.

Meenakshi is fond of collecting art pieces for decorating her house, for which she frequently
visits art exhibitions. Recently she bought a beautiful circular plate, which has beautiful
design carved between the inner and the outer circle. The inner circumference is 352mm and
outer is 396mm.
1. Find the inner radius. (1 Mark)
2. Find the outer radius. (1 Mark)
3. Find the width of the circular region with design. (2 Mark)

2.

Mr. Sohan Kumar is a very hard-working farmer. He owns a circular land of diameter 42m in
which he grows vegetables but many times some cows and goats of the village destroy his
vegetable garden. So, he decides to put a barbed fence all around his farmland.
1. What will be length of wire if he installs only one round of fencing wire.
2. Find the length of fencing wire needed if he makes 3 rounds of fence
3. Find the cost of the fencing wire if 1m of it cost ₹ 15.

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Answers

1. C 2. C 3. B 4. B
5. C 6. A 7. C 8. A
9. C 10. B

Short Answer Questions

1. 7cm 2. 14cm 3. 28cm,6cm2 4. 7cm
5. 10.5cm2 6. 75cm2 7. 2.5cm 8. 7cm
9. parallelogram 10. 18cm

Long Answer type Questions

1. ₹ 41.58 2. 1307cm2 3. 77cm2 4. 264m, ₹ 3168
5. 12m 6. 4.8m

Case Study Based Question

1. (I) 56mm (II) 63mm (III). 7mm
2. (I) 1386m (II) 4158m (III) ₹62,370

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Chapter Test-1
Perimeter and Area

Note: Q.1 to 4 are of1 mark each. M.M-20
Q.5 to 8 are of 2 marks each.
Q. 9 to 10 are of 4 marks each.
Q .1The area of a parallelogram of base 7cm and height 5cm is
(a) 70cm2 (b) 35cm2 (c) 50cm2 (d) 25cm2
Q.2 The area of a triangle of base 8cm and height 9cm is
(a) 36cm2 (b) 72cm2 (c) 91cm2 (d) 64cm2
Q.3 The circumference of circle of radius 7cm is
(a) 7cm (b) 22cm (c) 44cm (d) 88cm
Q.4 The area of circle of radius 7 units is
(a) 22 (b) 44 (c) 88 (d) 154
Q.5 What is the perimeter of a circular disc of diameter 10cm. (π = 3.14)
Q.6 What is the area occupied by a circle plate of diameter 21cm.
Q.7 Calculator the height of a parallelogram whose base is 10cm and area is 85cm2.
Q.8 Find the height of base a triangle of height 5cm and area 15cm2.
Q.9 What will be the area of a circular plate of circumference 38.5cm.
Q. 10. Case Study based Question.

Meera is very good in needle work and so wants to put a lace all around a plain while table cloth
which is circular in shape and of diameter 1m.
(a) Find the radius of the cloth. (1 Mark)
(b) Find the length of the lace required. (1 Mark)
(c) Find the cost of the lace if 1m of lace costs Rs. 17. (2 Mark)
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Chapter Test-2MM:30
Note: Q.1 to 5 are of1 mark each.Q.6 to 8 are of 2 marks each.Q. 9 to 10 are of 3 marks each.
Q. 11 to 12 are of 4 marks each Q. 13 is of 5 Marks.
Q.1The area of a semicircle of radius5cm is
(a) 78.5cm2 (b) 39.25cm2 (c) 25cm2 (d) 157cm2
Q.2 The circumference of a circle is always
(a) More than 3 times of its diameter (b) 3 times of its diameter
(c) Less than 3 times of its diameter (d) . times of its radius
Q.3 In reference to a circle the value of π is
(a) Area ÷circumference (b) Area ÷diameter
(c) Circumference ÷ diameter (d) Circumference ÷ radius
Q.4 Find the area of a parallelogram of base 4.2cm and height 10cm.
(a) 42cm2 (b) 10cm2 (c) 50cm2 (d) 25cm2
Q.5 Find the area of triangle of base 25cm and height 10cm
(a) 10cm2 (b) 25cm2 (c) 75cm2 (d) 125cm2
Q.6 If the radius of a circle is tripled by how many times will the area increase.
Q.7 What is the diameter is a circle whose area is 154cm2.
Q.8 One side of a parallelogram is 16cm and the distance of this side from the opposite side is 4.5cm.
Find the area of the parallelogram.
Q. 9 If the sides of a parallelogram are increased to twice its original lengths, how much will be the
perimeter of the new parallelogram.
Q. 10 What will be the area of a circle whose is 154cm2.
Q. 11 The perpendicular sides of a right triangle are 3cm and 4cm. What will be the increase in the
area
it these sides are doubled.
Q.12From a circular card board of radius 14cm, two circle of radius 1cm each, a triangle of base 1cm
and height 0.5cm and a rectangle of dimension 2cm, 1cm are removed. Find the area of the
remaining sheet.
Q.13 Case Study Based Question: A Circular lawn is enclosed by a
circular path all around it. The radius of the circular lawn is 1m.
While the radius of the outer circle including the path is 2m.
(a) Find the area of small circle (1 Mark)

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(b) Find the area of long of large circle (1 Mark)
(c) Find the width of the path and also its area (2 Mark)

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Study Materials
Notes

Model Papers Class 6 Notes

Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes

Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats

Maps of India / World Class 12 Notes

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