Area and Perimeter
x

Revision notes for Edexcel GCSE Maths Area and Perimeter. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Area and Perimeter

What you'll learn

  • Tell the distance around a shape from the space inside it.
  • Use simple rules for common shapes.
  • Draw shapes from area or perimeter clues.
  • Find missing heights when you know the area.

1. Area, perimeter and units

A unit tells you what is being measured, such as cm or m. A centimetre grid is a grid where each small square is 1 cm wide and 1 cm tall.

A formula is a shortcut rule for doing a calculation.

Definition

Area and perimeter

  • The perimeter is the total distance around the outside of a shape.

  • The area is the amount of space inside a shape.

Common Mistake

Check the units

Perimeter uses length units like cm or m. Area uses square units like cm² or m².

Example

Using a centimetre grid

  1. Imagine a rectangle on a grid is 4 squares across and 3 squares high.

A 4 cm by 3 cm rectangle on a centimetre grid showing 12 square centimetres inside and the outside edges for perimeter.

  1. The area is found by multiplying across by up:

    A=4×3=12A=4 \times 3=12A=4×3=12

  2. The perimeter is the outside distance: 4 cm + 3 cm + 4 cm + 3 cm.

  3. So the area is 12 cm² and the perimeter is 14 cm.

2. Rectangles and squares

A rectangle is a four-sided shape with four right angles. A right angle is an angle of 90°.

A square is a rectangle where all four sides are the same length.

Key Idea

Rectangle and square rules

  • For a rectangle with length lll and width www, the area is A=l×wA=l \times wA=l×w.

  • For a rectangle, the perimeter is P=2l+2wP=2l+2wP=2l+2w.

  • For a square with side length sss, the area is A=s2A=s^2A=s2 and the perimeter is P=4sP=4sP=4s.

Example

A square with a given area

  1. A square has area 49 cm². For a square, area means side times side.

A square with area 49 cm², with the equal side lengths to be found before using the perimeter rule.

  1. Find the number that multiplies by itself to make 49. That number is 7, so each side is 7 cm.

  2. Use the perimeter rule:

    P=4×7=28P=4 \times 7=28P=4×7=28

  3. The perimeter is 28 cm.

Drawing a rectangle from clues

Sometimes you are told how the length and width are connected.

Example

Drawing a rectangle from its perimeter

  1. A rectangle has perimeter 30 cm. Its length is twice its width.

A rectangle where the length is shown as two equal parts and the width as one part, matching a total perimeter of 30 cm.

  1. Think of the width as 1 part. Then the length is 2 parts.

  2. Around the rectangle you have width + length + width + length, so that is 1 + 2 + 1 + 2 = 6 parts.

  3. Each part is 30 ÷ 6 = 5 cm.

  4. The width is 5 cm and the length is 10 cm, so draw a rectangle 10 squares by 5 squares.

Tip

When drawing on a grid

Once you have found the side lengths, label them. This helps show the examiner that your drawing matches the clues.

3. Triangles and parallelograms

A base is the side you choose to measure along the bottom of a shape.

Perpendicular means meeting at a right angle. The perpendicular height is the straight distance from the base to the opposite side or corner.

Parallel lines are always the same distance apart and never meet. A parallelogram is a four-sided shape with opposite sides parallel.

Key Idea

Triangle and parallelogram areas

  • For a triangle with base bbb and perpendicular height hhh, the area is A=b×h2A=\frac{b \times h}{2}A=2b×h​.

  • For a parallelogram with base bbb and perpendicular height hhh, the area is A=b×hA=b \times hA=b×h.

Common Mistake

Use the straight height

For triangles, parallelograms and trapeziums, do not use a sloping side as the height unless it is at 90° to the base.

Example

Triangle and parallelogram areas

  1. A triangle on a grid has base 6 cm and perpendicular height 5 cm.

A triangle with base 6 cm and perpendicular height 5 cm, next to a parallelogram with base 4 cm and perpendicular height 7 cm.

  1. Use the triangle area rule:

    A=6×52=15A=\frac{6 \times 5}{2}=15A=26×5​=15

  2. A four-sided shape with opposite sides parallel is called a parallelogram.

  3. If the parallelogram has base 4 cm and perpendicular height 7 cm, use its area rule:

    A=4×7=28A=4 \times 7=28A=4×7=28

  4. The triangle has area 15 cm² and the parallelogram has area 28 cm².

Finding a missing height

The letter hhh is often used for an unknown height.

Example

Finding a missing parallelogram height

  1. A right-angled triangle has base 8 cm and height 3 cm. Its area is:

A right-angled triangle with base 8 cm and height 3 cm, alongside a parallelogram with base 9 cm and unknown height h.

$$
A=\frac{8 \times 3}{2}=12
$$

2. A parallelogram has base 9 cm. Its area is three times the triangle’s area.

  1. Three times 12 cm² is 36 cm².

  2. Use A=b×hA=b \times hA=b×h for the parallelogram:

    36=9h36=9h36=9h

  3. Divide by 9, so h=4h=4h=4. The height is 4 cm.

4. Compound shapes and perimeter

A compound shape is made by joining two or more simpler shapes. For perimeter, only count the outside edges.

Key Idea

Only count the outside

Edges where two shapes are joined are inside the shape, so they are not part of the perimeter.

Example

Perimeter of an L-shape

  1. Two identical rectangles are each 6 cm by 3 cm. They are joined along one 3 cm edge to make an L-shape.

Two 6 cm by 3 cm rectangles joined along a 3 cm edge to form an L-shape, with only the outside boundary counted for perimeter.

  1. One rectangle has perimeter:

    P=6+3+6+3=18P=6+3+6+3=18P=6+3+6+3=18

  2. Two separate rectangles would have 36 cm of edges altogether.

  3. The joined 3 cm edge has been counted twice, so subtract 6 cm.

  4. The perimeter of the L-shape is 30 cm.

5. Trapeziums

A trapezium is a four-sided shape with one pair of parallel sides. In area questions, use the two parallel side lengths and the perpendicular height.

Key Idea

Trapezium area

Add the two parallel sides, halve the answer, then multiply by the height:

A=12(a+b)hA=\frac{1}{2}(a+b)hA=21​(a+b)h
Example

Trapezium area and missing height

  1. A garden is a trapezium with parallel sides 7 m and 11 m, and height 5 m.

A trapezium garden with parallel sides 7 m and 11 m and perpendicular height 5 m.

  1. Add the parallel sides: 7 + 11 = 18.

  2. Halve that and multiply by the height:

    A=12×18×5=45A=\frac{1}{2}\times 18 \times 5=45A=21​×18×5=45

  3. The garden area is 45 m².

  4. Now suppose another trapezium has area 48 cm² and parallel sides 4 cm and 12 cm. Half the sum of the parallel sides is 8.

A second trapezium with area 48 cm² and unknown height h between parallel sides 4 cm and 12 cm.

  1. Solve for hhh:

    48=8h48=8h48=8h

  2. Divide by 8, so h=6h=6h=6. The height is 6 cm.

Exam technique

In the exam

  1. Underline whether the question asks for area or perimeter.

  2. Write the formula first, then put the numbers in carefully.

  3. Check your units: cm or m for perimeter, cm² or m² for area.

Self review

Check yourself

  • How do you find the area of a triangle?

  • Why is the sloping side of a parallelogram usually not the height?

  • If a square has perimeter 20 cm, what would you do first to find its area?

Recap questions

Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.

You've reached the end

Test yourself on this topic, or move on to the next guide.

Practice questionsTake a quick quiz on this topicFlashcardsSelf-test with active recall
ProbabilityUp next

How was this guide?

Area and Perimeter Revision Guide

  1. GCSE
  2. /Maths
  3. /Area and Perimeter