Area & Perimeter (CIE IGCSE Maths: Core)

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 4x 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

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 in 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

How do I find the area of a shape on a square grid?

• One of the simplest ways to calculate the area of a shape is using a square grid
• Simply count the total number of squares inside the shape
  • It is a good idea to shade or mark the squares you have counted so far
• There will be a scale, usually each square is 1 cm² (a square with sides of 1 cm) but do check this
• Often there will be parts of the shape which do not contain whole squares; they contain half-squares, where the square has been cut in half across its diagonal
  • Try to pair-up these half squares to form whole ones

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: