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

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2 Perimeters

One of the properties of a shape that is measured is its perimeter. This is the distance around the edge of a shape. For a shape with straight edges, you can work out the perimeter by measuring the length of each edge and then adding these together.

For example, one practical application of this would be someone wanting to decorate the room shown in Figure 12, using a border along the top of all the walls. To determine the length of the border they would need to work out the perimeter. So the border would measure:

five m prefix plus of four m prefix plus of five m prefix plus of four m equals 18 m

An alternative way to calculate this would be to note that the pairs of sides are the same length, giving us:

five m prefix multiplication of two plus four m prefix multiplication of two equals 18 m

This shows a rectangle.
Figure 12 What is the perimeter of this rectangle?
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This shows a rectangle. The lengths of the sides are marked as 5 m, 4 m, 5 m, and 4 m, working clockwise around the figure starting at the top edge.

Figure 12 What is the perimeter of this rectangle?

Have a go yourself in this next activity.

Activity 2 Around the edge

Timing: Allow approximately 5 minutes
  • a.This figure is formed from three of the shapes. What is its perimeter?
    Figure formed from three of the shapes
    Figure 13 Figure formed from three of the shapes
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    This shape has been formed by putting the square (piece 5) along the shorter side of the parallelogram (piece 3). One of the shorter sides of the triangle (piece 4) has been put next to the side of the square so that the long side of the parallelogram and the long side of the triangle lie in a straight line.

    Figure 13 Figure formed from three of the shapes

Answer

  • a.Starting on the left at the top of shape 3 and going clockwise around the figure, the perimeter is:

    five cm prefix plus of 3.5 cm prefix plus of 3.5 cm prefix plus of 3.5 cm prefix plus of five cm prefix plus of five cm prefix plus of 3.5 cm equals 29 cm

    You could have also shown the working as:

    three multiplication five cm prefix plus of four multiplication 3.5 cm equals 29 cm

When a shape has straight sides, you can measure the perimeter fairly easily by considering each side in turn. However, measuring lines that are not straight can be more difficult. If you need the measurement for some practical purpose, then you can use a piece of string to wrap around an object and then measure the string. However, as you’ll discover in the next section there more precise methods to calculate these in maths.