GCSE Maths grade 4 basics · topic 6 of 9

Area and perimeter: GCSE Maths grade 4 basics

Perimeter is the distance around the outside; area is the space inside. Learn the handful of area formulae, and always write the units.

Practise: 11 questions Read the basics first

In plain English

Perimeter: add up every side. Units are length units, like cm or m.
Area: rectangle = length × width; triangle = 1/2 × base × height; parallelogram = base × height; trapezium = 1/2 × (a + b) × height. Units are squared, like cm².
Circles: area = πr², circumference = πd (or 2πr). The radius is half the diameter.
Compound shapes: split them into rectangles and triangles, find each area, then add (or subtract a cut-out).

Worked example

A triangle has a base of 12 cm and a perpendicular height of 5 cm. Find its area.

Area = 1/2 × base × height
= 1/2 × 12 × 5
= 30 cm²

Answer: 30 cm²

Most common mistake

WrongArea of a triangle with base 10 cm and height 6 cm: 10 × 6 = 60 cm²

Right1/2 × 10 × 6 = 30 cm²

A triangle is half of a rectangle, so don't forget the half. Also use the perpendicular height (at right angles to the base), not a sloping side.

Practice questions (11)

Try each one on paper first, then open the worked answer and mark yourself. You don't need a calculator unless the question says so.

Q1.A rectangle is 8 cm long and 5 cm wide. Find its perimeter.
Show worked answer
1. Perimeter = 8 + 5 + 8 + 5
2. = 26 cm
Answer: 26 cm
Q2.Find the area of the same rectangle, 8 cm by 5 cm.
Show worked answer
1. Area = length × width = 8 × 5
2. = 40 cm²
Answer: 40 cm²
Q3.A triangle has a base of 10 cm and a perpendicular height of 6 cm. Find its area.
Show worked answer
1. Area = 1/2 × 10 × 6
2. = 30 cm²
Answer: 30 cm²
Q4.A parallelogram has a base of 9 m and a perpendicular height of 4 m. Find its area.
Show worked answer
1. Area = base × height = 9 × 4
2. = 36 m²
Answer: 36 m²
Q5.A trapezium has parallel sides of 6 cm and 10 cm. The height is 5 cm. Find its area.
Show worked answer
1. Area = 1/2 × (a + b) × h
2. = 1/2 × (6 + 10) × 5
3. = 1/2 × 16 × 5 = 40 cm²
Answer: 40 cm²
Q6.A square has an area of 49 cm². Find its perimeter.
Show worked answer
1. Side length = √49 = 7 cm
2. Perimeter = 4 × 7 = 28 cm
Answer: 28 cm
Q7.A circle has a radius of 5 cm. Find its area, to 1 decimal place. Calculator
Show worked answer
1. Area = πr² = π × 5²
2. = 25π = 78.539…
3. = 78.5 cm² (1 d.p.)
Answer: 78.5 cm²
Q8.A circle has a diameter of 10 cm. Find its circumference, to 1 decimal place. Calculator
Show worked answer
1. Circumference = π × d = π × 10
2. = 31.415…
3. = 31.4 cm (1 d.p.)
Answer: 31.4 cm
Q9.An L-shape is made by cutting a 4 cm by 3 cm rectangle from the corner of a 10 cm by 6 cm rectangle. Find the area of the L-shape.
Show worked answer
1. Big rectangle: 10 × 6 = 60 cm²
2. Cut-out: 4 × 3 = 12 cm²
3. L-shape: 60 − 12 = 48 cm²
Answer: 48 cm²
Q10.A rectangular garden is 12 m by 7 m. Turf costs £4 per m². How much does it cost to turf the whole garden?
Show worked answer
1. Area = 12 × 7 = 84 m²
2. Cost = 84 × £4 = £336
Answer: £336
Q11.A rectangle has an area of 36 cm² and a length of 9 cm. Find its width.
Show worked answer
1. Area = length × width, so width = area ÷ length
2. 36 ÷ 9 = 4 cm
Answer: 4 cm

Can you do these?

Find the perimeter of a shape
Find the area of rectangles, triangles, parallelograms and trapeziums
Find the area and circumference of a circle
Find the area of a compound shape, with the right units

Tick them off on the printable checklist. Want more? The Core sections of our free area and perimeter notes cover the same maths (they are written for IGCSE, but the basics are the same).