GCSE Maths → Geometry → Area and Perimeter

Area and Perimeter GCSE Maths

Area and perimeter are key GCSE geometry skills. Perimeter is the distance around the outside of a shape. Area is the space inside a shape.

Many students lose marks because they mix up area and perimeter, use the wrong units, or forget to split compound shapes into simpler shapes.

Video explanation

A short Worthing Maths Tutor video explanation for area and perimeter GCSE maths can be embedded here later to improve student engagement and time on page.

Area vs perimeter

Perimeter = distance around the outside
Area = space inside the shape

Exam tip: Perimeter uses units like cm or m. Area uses square units like cm² or m².

Perimeter of rectangles

Example 1: Perimeter of a rectangle

A rectangle has length 8 cm and width 5 cm.

Add all four sides:

8 + 5 + 8 + 5 = 26

The perimeter is 26 cm.

Area of rectangles

For a rectangle:

area = length × width

Example 2: Area of a rectangle

A rectangle has length 8 cm and width 5 cm.

area = 8 × 5 = 40

The area is 40 cm².

Common mistake: Do not write the area as 40 cm. Area must be written in square units: 40 cm².

Area of triangles

For a triangle:

area = 1/2 × base × height

Example 3: Area of a triangle

A triangle has base 10 cm and height 6 cm.

area = 1/2 × 10 × 6

area = 30

The area is 30 cm².

Exam tip: The height must be perpendicular to the base. Do not use a slanted side as the height unless it is actually perpendicular.

Compound shapes

Compound shapes are made from two or more simpler shapes. Split the shape into rectangles, triangles, or other familiar shapes.

Example 4: Compound shape made from rectangles

A compound shape is made from two rectangles. One rectangle has area 6 × 4 = 24 cm². The other has area 3 × 5 = 15 cm².

Add the areas:

24 + 15 = 39

The total area is 39 cm².

Area and circumference of circles

For a circle:

circumference = πd
area = πr²

Example 5: Circumference of a circle

A circle has diameter 10 cm.

circumference = π × 10 = 31.4 cm

to 1 decimal place.

Example 6: Area of a circle

A circle has radius 4 cm.

area = π × 4²

area = 16π = 50.3 cm²

to 1 decimal place.

Common mistake: In area of a circle, square the radius, not the diameter.

Common mistakes in area and perimeter

Mixing up area and perimeter.
Using cm instead of cm² for area.
Forgetting to add all outside edges for perimeter.
Using a slanted side as the height of a triangle.
Using diameter instead of radius in πr².
Forgetting to split compound shapes clearly.

Practice questions

Find the perimeter of a rectangle with length 9 cm and width 4 cm.
Find the area of a rectangle with length 9 cm and width 4 cm.
Find the area of a triangle with base 12 cm and height 5 cm.
Find the circumference of a circle with diameter 8 cm. Give your answer to 1 decimal place.
Find the area of a circle with radius 5 cm. Give your answer to 1 decimal place.

Answers

26 cm
36 cm²
30 cm²
25.1 cm
78.5 cm²

Area and perimeter FAQ

What is the difference between area and perimeter?

Perimeter is the distance around the outside of a shape. Area is the space inside a shape.

What units are used for area?

Area is measured in square units, such as cm², m², or mm².

What units are used for perimeter?

Perimeter is measured in length units, such as cm, m, or mm.

Are area and perimeter on GCSE maths?

Yes. Area and perimeter are common GCSE maths topics and often appear in compound shape, circle, and worded exam questions.

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