Find the perimeter and area of rectangles, triangles, parallelograms and trapeziums, and use them in cost problems. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Perimeter is the distance around the outside — add every outer edge, and do not count a cut-out edge as outside if it is no longer on the boundary. Area is the space inside. Rectangle: length × width. Parallelogram: base × perpendicular height (not the slanting side). Triangle: 21× base × perpendicular height. Square: side squared, so if the perimeter is 36 cm the side is 9 cm and the area is 81 cm².
Compound L-shapes are a big rectangle minus a small one, or two rectangles added. A 10 by 8 rectangle with a 4 by 3 bite taken out has area 80−12=68 cm². Sketch the missing rectangle on the diagram so you do not subtract the wrong pair of sides.
Units: perimeter in cm, area in cm². Mixing them is a free mark given away.
Objectives
Add every outside edge.
Area of a rectangle is length times width.
Perimeter is in cm or m. Area is in cm² or m².
Key points
Tell the difference between perimeter (distance round the edge) and area (space inside).
Use the area formulae for a rectangle, triangle, parallelogram and trapezium.
Use the perpendicular height, not a sloping side, in the area formulae.
Split a compound (L-shaped) shape into rectangles and add the areas.
Worked examples
Example 1
A rectangle is 3 cm by 4 cm. What is its area in cm²?
2 marks
Rectangle area is length × width, so the area is 3 × 4.
3 × 4 = 12.
The area is 12 cm².
Answer: 12 cm²
Common slips
Slip: Rectangle area is length × width, so the area is 5 × 4. That changes a number from the question, so it answers a different question.
Slip: 3 + 4 = 7. That uses addition, but this step needs multiplication.
Slip: The area is 16 cm². That does not match the working above it.
Example 2
A triangle has base 6 cm and perpendicular height 4 cm. What is its area in cm²?
2 marks
Triangle area is half of base × height: 6 × 4 = 24.
Half of 24 is 12.
The area is 12 cm².
Answer: 12 cm²
Common slips
Slip: Triangle area is half of base × height: 8 × 4 = 24. That changes a number from the question, so it answers a different question.
Slip: Half of 27 is 12. That changes a number in the working, so the step no longer follows from the one before.
Slip: The area is 16 cm². That does not match the working above it.
Example 3
A rectangle is 8 cm long and 3 cm wide. What is its perimeter in cm?
2 marks
Length plus width: 8 + 3 = 11.
Opposite sides match, so double it: 11 × 2 = 22.
The perimeter is 22 cm.
Answer: 22 cm
Common slips
Slip: Length plus width: 10 + 3 = 11. That changes a number from the question, so it answers a different question.
Slip: Opposite sides match, so double it: 14 × 2 = 22. That changes a number in the working, so the step no longer follows from the one before.
Slip: The perimeter is 26 cm. That does not match the working above it.
Questions and answers
GCSE Maths area & perimeter questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A rectangle is 6 cm by 4 cm. What is its area?
Show answer
Answer: 24
Multiply the length by the width.
The value is 24.
M1 — Multiply the length by the width.
A1 — Answer 24
Question 2 Easy2 marks
A rectangle is 8 cm by 3 cm. What is its perimeter?
Show answer
Answer: 22
Add the length and width.
Double that sum.
M1 — Add the length and width.
A1 — Answer 22
Question 3 Medium2 marks
A rectangle has area 24 cm² and width 3 cm. What is the length?
Show answer
Answer: 8
Divide the area by the width.
The value is 8.
M1 — Divide the area by the width.
A1 — Answer 8
Question 4 Medium2 marks
A triangle has area 30 cm² and base 10 cm. What is the height?
Show answer
Answer: 6
Double the area, then divide by the base.
The value is 6.
M1 — Double the area, then divide by the base.
A1 — Answer 6
Question 5 Hard2 marks
A floor is 5 m by 4 m. Tiles cost £3 per square metre. What is the cost?
Show answer
Answer: 60
Find the area first.
Then multiply by the price.
M1 — Find the area first.
A1 — Answer 60
Question 6 Hard2 marks
A rectangular field is 12 m by 7 m. A path runs around all four sides. How long is the path?
Show answer
Answer: 38
The path is the perimeter.
The value is 38.
M1 — The path is the perimeter.
A1 — Answer 38
Question 7 Exam-style3 marks
A floor is 6 m by 4 m. Tiles cost £3 per square metre. What is the cost?
Show answer
Answer: 72
Find the area first.
Then multiply by the price.
M1 — Find the area first.
M1 — Then multiply by the price.
A1 — Answer 72
Common mistakes
Most lost marks on this topic are one slip.
Adding the sides to find area.
Rectangle area is length times width.
Forgetting half in a triangle.
Triangle area is half of base times perpendicular height.
Giving area in cm instead of cm².
Area uses square units.
Spot the slip
The perimeter of a shape is
the distance around the outside
the space inside
the longest side
Show the slip
the distance around the outside You walk the boundary to measure perimeter.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the formula before you substitute; even with a slip in the arithmetic you keep the method mark.
Mark the perpendicular height on the diagram with a right-angle symbol so you use the correct length.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.