Chapter 25

Areas of common shapes

25.1 Introduction

Areais a measure of the size or extent of a plane surface.
Area is measured insquare unitssuch as mm^2 ,cm^2 and
m^2. This chapter deals with finding the areas of common
shapes.
In engineering it is often important to be able to cal-
culate simple areas of various shapes. In everyday life
its importantto be able to measure area to, say, lay a car-
pet, order sufficient paint for a decorating job or order
sufficient bricks for a new wall.
On completing this chapter you will be able to recog-
nize common shapes and be able to find the areas of rect-
angles, squares, parallelograms, triangles, trapeziums
and circles.

25.2 Common shapes

25.2.1 Polygons

A polygon is a closed plane figure bounded by straight
lines. A polygon which has
3 sides is called atriangle– see Figure 25.1(a)
4 sides is called aquadrilateral– see Figure 25.1(b)
5 sides is called apentagon– see Figure 25.1(c)
6 sides is called ahexagon– see Figure 25.1(d)
7 sides is called aheptagon– see Figure 25.1(e)
8 sides is called anoctagon– see Figure 25.1(f)

25.2.2 Quadrilaterals

There are five types of quadrilateral, these being rect-
angle, square, parallelogram, rhombus and trapezium.
If the opposite corners of any quadrilateral are joined
by a straight line, two triangles are produced. Since the
sum of the angles of a triangle is 180◦, the sum of the
angles of a quadrilateral is 360◦.

Rectangle

In the rectangleABCDshown in Figure 25.2,

(a) all four angles are right angles,

(b) the opposite sides are parallel and equal in length,

and

(c) diagonalsACandBDare equal in length and bisect

one another.

Square

In the squarePQRSshown in Figure 25.3,

(a) all four angles are right angles,

(b) the opposite sides are parallel,

(c) all four sides are equal in length, and

(d) diagonalsPRandQSare equal in lengthand bisect

one another at right angles.

Parallelogram

In the parallelogramWXYZshown in Figure 25.4,

(a) opposite angles are equal,

(b) opposite sides are parallel and equal in length, and

(c) diagonalsWYandXZbisect one another.

Rhombus

In the rhombusABCDshown in Figure 25.5,

(a) opposite angles are equal,

(b) opposite angles are bisected by a diagonal,

(c) opposite sides are parallel,

(d) all four sides are equal in length, and

(e) diagonalsACandBDbisect one another at right

angles.

DOI: 10.1016/B978-1-85617-697-2.00025-9