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Area & Perimeter

Perimeter

What is perimeter?

  • Perimeter is the total distance around the outside of a 2D shape
  • It is found by adding the lengths of the sides together
  • The perimeter of a circle is called the circumference

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

  • To find the perimeter of any 2D polygon, add the lengths of its sides together
  • 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 4 x cm
  • Often, the shape will not be a straight-forward 2D shape and you will need to use the information given to find the lengths of some of the sides
    • Shapes made up of 2 or more 2D shapes are called compound shapes
  • If the compound shape is made up of two rectangles, for example an L-shape, the length of two shorter sides opposite a longer side will add up to the same as the longer side
  • If the compound shape is made up of other 2D shapes, you will need to use more information to find the lengths of the individual sides
    • To do this you will need to be confident with the properties of 2D shapes
    • 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

Exam Tip

  • Understanding how to find missing lengths of compound shapes can be essential for questions involving forming algebraic equations
  • Try it with numbers and then see how that can be transferred to working with algebraic expressions

Worked example

The compound shape below consists of a rectangle with length 5 cm and width 4 cm and a second rectangle of length 15 cm and width 6 cm.

Find the perimeter of the compound shape.

3-5-perimeter-we-diagram

The shape is made up of two rectangles, so all sides meet at right angles
The two shorter sides at the top will be equal to the 15 cm length at the bottom
The missing side on the left will be equal to the sum of the two shorter sides on the right

3-5-perimeter-we-solution-image

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

P = 5 + 4 + 10 + 6 + 15 + 10 cm

You could also instead consider the four sides of the new, biggest rectangle

P = 2(10 + 15) cm

P = 50 cm

Area Formulae

What is area and why do we need to calculate it?

  • Area is the amount of space taken up by a two-dimensional shape
  • Volume deals with three-dimensional shapes and space
  • Some of the uses of area are a little more obvious than some areas of maths
    • Examples include working out the area of a floor if laying a new carpet or the amount of land needed if designing a sports field

Area – using formulae

  • There are some basic formulae you should know and be comfortable using
  • Be aware that some area formulae use distances that aren’t necessarily one of the sides of the shape
  • Make sure you know what the different letters in each formula are referring to
  • These formulae are essential – anything more complicated will be given in the exam:

Area-Formulae---2D, IGCSE & GCSE Maths revision notes

Exam Tip

  • You may have to do some work to find the lengths first, e,g, using Pythagoras’ Theorem, Trigonometry (SOHCAHTOA) etc

Worked example

The cross section of a sculpture consists of a trapezium, a parallelogram, and a right-angled triangle.

Its dimensions are shown below

3-5-area-formulae-we-diagram

Find the total area of the cross section of the sculpture.

Find the area of the trapezium using 1 half open parentheses a plus b close parentheses h

1 half open parentheses 30 plus 15 close parentheses cross times 20 equals 450 space cm squared

Find the area of the parallelogram using  b cross times h.

15 cross times 12 equals 180 space cm squared

Find the area of the right-angled triangle using  1 half b h.

1 half cross times 8 cross times 7 equals 28 space cm squared

Find the total area

450 + 180 + 28

658 cm 2

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