Area & Perimeter (Edexcel GCSE Maths: Foundation)

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

What is area?

• Area is the amount of space within the perimeter of a 2D shape
  
  • For example, the size of a sports field
• Area is calculated using lengths in two dimensions
  • Units of measure include mm², cm², m² etc

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

• Count the total number of whole squares inside the shape
  • You can shade or mark the squares you have counted so far
• Parts of the shape may not contain whole squares
  • Pair up half squares, or parts of squares, to form whole ones
• There will be a scale telling you how much area one square represents
  
  • Multiply the number of squares you have counted by this value to find the total area of the shape

Which area formulae do I need to know?

How do I find the area of a rectangle?

• The area, A, of a rectangle of length, l, and width, w, using the formula
  • 
    • Multiply together the length and the width

How do I find the area of a triangle?

• The area, A, of a triangle with base, b, and length, l, can be found using the formula
  • 
    • Multiply the length of the base (b) by the perpendicular height (h)
    • Halve the answer
• The perpendicular height may not be the length of one of the sides of the triangle

How do I find the area of a trapezium?

• The area, A, of a trapezium with parallel lengths, a and b, and perpendicular height, h, can be found using the formula
  • 
    • Add together the lengths of the parallel sides
    • Multiply the result by the distance between the parallel sides
    • Halve the answer
• You may be able to work out the area of a trapezium by splitting the shape into a rectangle and triangles if you can't remember the formula

How do I find the area of a parallelogram?

• You can find the area, A, of a parallelogram of length, l, and perpendicular height, h, by using the formula
  •  
    • Multiply the length of the base by the perpendicular height
• The perpendicular height is not a length of the parallelogram
• • It is the distance between the base and its opposite side
• You can work the area of a parallelogram out by splitting the shape into a rectangle and triangles if you can't remember the formula