NCERT Book Class 8 Maths Chapter 9 Mensuration

MENSURATION 103

CHAPTER

Mensuration
9
9.1 Introduction
We have learnt that for a closed plane figure, the perimeter is the distance around its
boundary and its area is the region covered by it. We found the area and perimeter of
various plane figures such as triangles, rectangles, circles etc. We have also learnt to find
the area of pathways or borders in rectangular shapes.
In this chapter, we will try to solve problems related to perimeter and area of other
plane closed figures like quadrilaterals.
We will also learn about surface area and volume of solids such as cube, cuboid and
cylinder.
9.2 Area of a Polygon
We split a quadrilateral into triangles and find its area. Similar methods can be used to find
the area of a polygon. Observe the following for a pentagon: (Fig 9.1, 9.2)

Fig 9.1
Fig 9.1
By constructing one diagonal AD and two
By constructing two diagonals AC and AD the perpendiculars BF and CG on it, pentagon ABCDE is
pentagon ABCDE is divided into three parts. divided into four parts. So, area of ABCDE = area of
So, area ABCDE = area of ∆ ABC + area of right angled ∆ AFB + area of trapezium BFGC + area
∆ ACD + area of ∆ AED. of right angled ∆ CGD + area of ∆ AED. (Identify the
parallel sides of trapezium BFGC.)