Area

Exam code: 4024

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

Area Formulas

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

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

The area, A, of a rectangle of length, l, and width, w, using the formula
- $A = l \times w$
  - Multiply together the length and the width

The area, A, of a triangle with base, b, and length, l, can be found using the formula
- $A = \frac{1}{2} b h$
  - Multiply the length of the base (b) by the perpendicular height (h)
  - Halve the answer
The formula for the area of a triangle is given to you in the exam
The perpendicular height may not be the length of one of the sides of the triangle

The area, A, of a trapezium with parallel lengths, a and b, and perpendicular height, h, can be found using the formula
- $A = \frac{1}{2} (a + b) h$
  - 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

You can find the area, A, of a parallelogram of length, l, and perpendicular height, h, by using the formula
- $A = b h$
  - 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

Worked example

Calculate the area of the following shapes.

(a)

Find the area of the trapezium using $A = \frac{1}{2} (a + b) h$

Answer:
Remember that a and b are the two parallel sides and h is the perpendicular height

$A = \frac{1}{2} (30 + 15) \times 20$

450 cm²

(b)

Find the area of the parallelogram using $A = b \times h$

Answer:

Remember that b is the base and h is the perpendicular height

$A = 15 \times 12$

180 cm²

(c)

Find the area of the right-angled triangle using $A = \frac{1}{2} b h$

Answer:

Remember that b is the base and h is the perpendicular height

$A = \frac{1}{2} \times 8 \times 7$

28 cm²

Area Formulas