GCSE Maths Area & Perimeter Notes
Perimeter is the distance around a shape; area is the space inside it. Each 2D shape has its own area formula, and circles use π.
Key concepts
- Perimeter
- Add up the lengths of all the sides. For a circle this is the circumference.
- Area of a rectangle
- Length × width — the number of unit squares that fit inside.
- Area of a triangle
- Half the base times the perpendicular height.
- Circle measures
- Circumference = πd and area = πr² — remember d = 2r.
Key formulas
Rectangle area
A = length × width
Triangle area
A = ½ × base × height
Circle area
A = πr²
Circumference
C = πd = 2πr
Worked example
Find the area of a circle with radius 5 cm (to 1 d.p.).
- 1Use A = πr².
- 2Substitute r = 5: A = π × 5² = π × 25.
- 3Work it out: 25 × 3.14159… = 78.53981…
- 4Round to 1 decimal place: 78.5 cm².
Answer: 78.5 cm²
Common mistakes
✗ Using diameter instead of radius in πr².
✓ The area formula needs the radius; halve the diameter first.
✗ Forgetting the ½ in the triangle area.
✓ Area of a triangle is half base times height.
✗ Giving area in cm instead of cm².
✓ Area is always in square units.
Quick check
Try these, then reveal the answers.
Area of a 6 cm by 4 cm rectangle?Reveal answer
24 cm²
Area of a triangle base 10, height 3?Reveal answer
15
Circumference of a circle radius 7 (use π)?Reveal answer
14π ≈ 44.0
Exam tips
- Split compound shapes into rectangles and triangles you know.
- Keep answers in terms of π if the question does not ask for a decimal.
- Always add the correct square units to an area answer.
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Frequently asked questions
What is the difference between area and perimeter?+
Perimeter is the total distance around the edge; area is the amount of space inside the shape.
How do I find the area of a circle?+
Square the radius and multiply by π: A = πr².
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