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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
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Exam code:8300

Perimeter

What is perimeter?

  • Perimeter is the total distance around the outside of a 2D shape

    • The perimeter of a circle is called the circumference

  • Perimeter is a length in one dimension

    • Units of measure include mm, cm, m etc

How do I find the perimeter of a 2D shape?

  • Add together the lengths of all of the sides of the shape

  • For any regular 2D shape, the perimeter will be the number of sides, multiplied by the length of one side

    • For example, the perimeter of a square of side length x cm will be 4x cm

How do I find the perimeter of a compound shape?

  • Shapes may be made up of two or more 2D shapes, these are called compound shapes

    • Compound shapes can usually be split into rectangles, triangles and parts of circles

    • You will need to be confident with the properties of 2D shapes

      • For example, the distance between the centre point of a circle and a point on the circumference is its radius

    • Look out for sides that are equal, for example in a rectangle, parallelogram, or isosceles triangle

      • Dashes may be used to mark the equal sides, or the question may tell you which sides are equal

    • You may need to use certain formulas to calculate lengths

      • For example, you may need to use Pythagoras’ theorem to calculate a length on a right-angled triangle

    • You may need to use the given information to find the lengths of some of the sides

      • For example, the L-shape below can be split into two rectangles

      • The sum of the lengths of two shorter sides will be the same as the length of the longer side opposite

A compound shape split into two rectangles

Examiner Tips and Tricks

  • Understanding properties of different 2D shapes can be essential for missing lengths.

Worked Example

Find the perimeter of the compound shape.

A compound shape made up of rectangles and an isosceles triangle

The shape can be split up into a triangle and two rectangles

The dashes on the triangle mean that the lengths are equal
It is an isosceles triangle and the missing length is 6 cm

The horizontal lengths of the two rectangles add up to the length of the longest horizontal line
15 cm and the missing length, are equal to the 18 cm length at the top
The missing horizontal length is therefore 3 cm 

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You can now find the sum of all the sides to find the total perimeter

6 + 6 + 18 + 2 + 3 + 4 + 15

54 cm

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