Areas of Composite Shapes

Areas of Composite Shapes

GCSE(F),

A Compound Shape is a shape that is built up from two or more Simple Shapes. A simple shape is a shape for which formula for calculating area are readily available such as triangles, rectangles, circles, and so on.

To calculate the area of a complex shape, divide the complex shape into a number of simple shapes. There are often a number of ways to divide the shape up: it does not matter which combination is used so long as the whole complex shape is taken into account.

The area of each simple shape is calculated separately; then added together as a total for the compound shape.

Examples

1. What is the area of this shape?

Answer: 160 cm2

Split the compound shape into two simple shapes: a rectangle and a triangle:

The area of the rectangle part is 12 x 10 = 120 cm2.

The missing dimension for the triangle part is 20 - 12 = 8cm.

Area of a triangle = `frac(1)(2)bh`

Area of triangle = `frac(1)(2) xx 10 xx 8 = 40` cm^2^.

Area of compound shape = area of rectangle + area of triangle = 120 + 40 = 160 cm^2^.

2. A stained glass window is being manufactured as the centrepiece of a new home. The stained glass will cost £250 per square metre. How much will the stained glass cost for the window?

Answer: £1062.50

The lower part of the window is a rectangle:

Area of a rectangle = b x h = 2 x 1.34 = 2.68 cm2.

The upper part of the window is a semicircle (half a circle).

The diameter of the semicircle is the width of the window; the radius is half of that = 1m.

Area of a whole circle = πr2:

Area of this semicircle = `frac(1)(2) xx π xx 1^2 = 1.57 m^2`

Area of entire window = 2.68 + 1.57 = 4.25 m2

Cost of window = 250 x 5.82 = £1062.50