Find the perimeter of the rectangle.
Perimeter means distance around the outside.
Perimeter = 10 + 5 + 10 + 5 = 30 cm.
Perimeter and Area
Perimeter measures the distance around a shape, while area measures the space inside it. These calculations are essential for geometry and link directly to 3D shapes and circle properties.
Overview
Perimeter and area measure different things.
Perimeter is the distance around the outside of a shape.
Area is the space inside the shape.
A very common exam mistake is using an area formula when the question asks for perimeter, or giving area without square units.
What you should understand after this topic
- Understand the difference between perimeter and area
- Calculate perimeter of common shapes
- Calculate area of rectangles, triangles and parallelograms
- Calculate area of compound shapes
- Use the correct units in answers
Perimeter
Distance around the edge of a shape.
Area
Space inside a shape.
Key Definitions
Perimeter
The total distance around the outside of a shape.
Area
The amount of space inside a 2D shape.
Square Units
Units used for area, such as cm² or m².
Linear Units
Units used for perimeter, such as cm or m.
Base
The chosen bottom side of a shape, often used in area formulas.
Height
The perpendicular distance from the base to the top.
Key Rules
Perimeter means outside only
Add the lengths around the edge of the shape.
Area means inside space
Use an area formula that matches the shape.
Use square units for area
For example, cm², m² or mm².
Height must be perpendicular
For triangle and parallelogram area, use the perpendicular height.
Common 2D Shapes
Rectangle
Perimeter and area both appear often.
Triangle
Area uses half of base × height.
Parallelogram
Area is base × perpendicular height.
Compound shape
Split into smaller known shapes first.
How to Solve
Step 1: Identify perimeter or area
First check what the question is asking.
Exam tip: Always check the units — this tells you what to calculate.
Perimeter
Total distance around a shape (units: cm, m).
Area
Space inside a shape (units: cm², m²).
Step 2: Know key formulas
Rectangle: \(A = l \times w\)
Triangle: \(A = \frac{1}{2}bh\)
Parallelogram: \(A = bh\)
Trapezium: \(A = \frac{1}{2}(a+b)h\)
Circle: \(A = \pi r^2\), \(C = 2\pi r\)
Exam tip: Always use the perpendicular height.
Step 3: Calculate perimeter
Add all outer sides.
Rectangle: \(2l + 2w\)
Include all edges — even hidden or split ones.
Important: Find any missing sides first.
Step 4: Calculate area
Use the correct formula and multiply carefully.
Check you are using the correct measurements.
Always include square units (cm², m²).
Step 5: Compound shapes
Break the shape into simpler parts.
Exam thinking: Draw lines to divide the shape clearly.
- Split into rectangles or triangles.
- Find each area separately.
- Add or subtract areas.
Step 6: Circles
Use π formulas for circular shapes.
\( A = \pi r^2 \)
\( C = 2\pi r \)
Exam tip: Check if radius or diameter is given.
Circle problems often link to circle theorems.
Step 7: Exam method summary
See 3D shapes for surface area and volume.
- Identify the shape and what is required.
- Write the correct formula.
- Substitute values carefully.
- Calculate accurately.
- Check units (cm or cm²).
Example Questions
Edexcel
Exam-style questions focusing on perimeter and area of rectangles.
Edexcel
A rectangle has length 6 cm and width 3 cm.
Find the perimeter of the rectangle.
Edexcel
A rectangle has length 6 cm and width 3 cm.
Find the area of the rectangle.
AQA
Exam-style questions focusing on area of triangles and parallelograms.
AQA
A triangle has base 8 cm and height 5 cm.
Find the area of the triangle.
AQA
A parallelogram has base 7 cm and perpendicular height 4 cm.
Find the area of the parallelogram.
OCR
Exam-style questions focusing on units and compound areas.
OCR
Perimeter measures distance around a shape. Area measures the surface inside a shape.
Explain why area is written in cm² but perimeter is written in cm.
OCR
A compound shape is made from two rectangles with areas 15 cm² and 18 cm².
Find the total area.
OCR
The compound shape is made from two rectangles.
Describe how you could find the area of this compound shape.
Exam Checklist
Step 1
Check whether the question asks for perimeter or area.
Step 2
Choose the correct formula for the shape.
Step 3
Use the perpendicular height if needed.
Step 4
Write the correct units at the end.
Most common exam mistakes
Wrong measure
Using area when the question asks for perimeter.
Wrong units
Forgetting to square the units for area.
Wrong height
Using a sloping side instead of the perpendicular height.
Missed edge
Leaving out one side when finding perimeter.
Common Mistakes
These are common mistakes students make when calculating perimeter and area in GCSE Maths.
Confusing perimeter and area
Incorrect
A student uses an area formula when asked for perimeter, or vice versa.
Correct
Perimeter is the total distance around a shape, while area is the space inside. Always check what the question is asking.
Forgetting square units
Incorrect
A student gives area with units like cm instead of \(\text{cm}^2\).
Correct
Area is measured in square units, such as \(\text{cm}^2\) or \(\text{m}^2\). Always include the correct units.
Using a slanted side instead of height
Incorrect
A student uses the length of a slanted side in place of the perpendicular height.
Correct
Area formulas require the perpendicular height. Make sure you use the vertical height, not a sloping side.
Missing a side in the perimeter
Incorrect
A student forgets to include one or more sides when adding lengths.
Correct
Check that every side has been included. Mark the sides as you go to avoid missing any.
Not splitting compound shapes correctly
Incorrect
A student divides a shape incorrectly or misses part of it.
Correct
Split compound shapes into simple shapes such as rectangles and triangles. Calculate each area separately and then combine them.
Try It Yourself
Practise calculating the perimeter and area of 2D shapes.
Foundation
Foundation Practice
Calculate perimeter and area of rectangles, triangles and simple compound shapes.
Find the area of the rectangle.
Area of rectangle = length × width.
8 × 4 = 32 cm².
Find the area of the triangle.
Area of triangle = 1/2 × base × height.
1/2 × 12 × 7 = 42 cm².
A square has side length 6 cm. Find its perimeter.
A square has 4 equal sides.
4 × 6 = 24 cm.
A square has side length 9 cm. Find its area.
Area of square = side × side.
9 × 9 = 81 cm².
Find the perimeter of the triangle.
Add all three side lengths.
10 + 8 + 8 = 26 cm.
Which formula gives the area of a rectangle?
Area measures the space inside.
Area of a rectangle = length × width.
Find the area of a parallelogram with base 10 cm and height 6 cm.
Area of parallelogram = base × height.
10 × 6 = 60 cm².
Find the area of the parallelogram.
Use base × perpendicular height, not the slanted side.
Area = 9 × 4 = 36 cm².
A rectangle has area 45 cm² and length 9 cm. Find its width.
Width = area ÷ length.
45 ÷ 9 = 5 cm.
Higher
Higher Practice
Solve multi-step perimeter and area problems, including compound shapes and trapezia.
Find the area of the trapezium.
Area of trapezium = 1/2 × (a + b) × h.
1/2 × (8 + 14) × 5 = 55 cm².
Find the area of a trapezium with parallel sides 6 cm and 12 cm, and height 5 cm.
Use 1/2 × (a + b) × h.
1/2 × (6 + 12) × 5 = 45 cm².
Find the area of the compound L-shape.
Split into two rectangles: top rectangle and left lower rectangle.
Top rectangle: 9 × 3 = 27. Lower rectangle: 3 × 5 = 15. Total = 42 cm².
A compound shape is made from a 10 cm by 6 cm rectangle with a 4 cm by 2 cm rectangle removed. Find the remaining area.
Find the large area, then subtract the missing area.
10 × 6 = 60 and 4 × 2 = 8, so 60 − 8 = 52 cm².
Find the perimeter of the compound shape.
Add every outside edge.
12 + 4 + 6 + 8 + 6 + 12 = 48.
A rectangle has perimeter 34 cm. Its length is 11 cm. Find its width.
Perimeter = 2(length + width).
34 ÷ 2 = 17, so width = 17 − 11 = 6 cm.
A triangle has area 48 cm² and base 12 cm. Find its height.
Area = 1/2 × base × height.
48 = 1/2 × 12 × h, so 48 = 6h and h = 8 cm.
A parallelogram has area 72 cm² and base 12 cm. Find its perpendicular height.
Height = area ÷ base.
72 ÷ 12 = 6 cm.
A student calculates the area of a triangle using base × height only. What is wrong?
A triangle is half of a rectangle or parallelogram.
Triangle area = 1/2 × base × height.
The area of a square is 64 cm². Find its perimeter.
Find the side length first.
Side length = 8 cm, so perimeter = 4 × 8 = 32 cm.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What is perimeter?
The distance around a shape.
What is area?
The space inside a shape.
What is a common mistake?
Mixing up area and perimeter formulas.