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Succeed with maths: part 2
Succeed with maths: part 2

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2.3 Perimeters of mixed shapes

Suppose the shape that you wanted to determine the perimeter of is as shown in Figure 15.

A shape formed of a rectangle and two semicircles.
Figure 15 A shape formed of a rectangle and two semicircles

Start by noticing that the shape is formed of one rectangle and two semicircles. The distance around the two semicircles combined is the same as around a circle with a diameter of 1.6 m. So, calculating the circumference of a circle with this diameter will give us part of the answer. To find the total distance, or perimeter, you then just need to add in the lengths of the longest edges of the rectangle. This gives us the following calculation:

multiline equation line 1 Circumference of circle equals pi multiplication diameter line 2 equation left hand side equals right hand side pi multiplication 1.6 m line 3 equals 5.03 m left parenthesis to two decimal places right parenthesis

multiline equation line 1 Total perimeter equals 5.03 m prefix plus of two multiplication two m line 2 equals 9.03 m left parenthesis to two decimal places right parenthesis

So, if you are faced with a complex shape, look for ways to split these up to help you calculate the perimeter.

Another property of a shape that can be useful to know is the area, or space that it occupies. This is slightly more complicated than the perimeter, but for regular shapes there are a set of formulas to help with this, as you will see in the next section.