Sheet № 44 · Foundation + Higher · AQA · Edexcel · OCR
Area of 2D Shapes
Calculating the area of two-dimensional shapes is one of the most essential skills in GCSE Maths. It appears across every paper and every exam board — AQA, Edexcel and OCR — from straightforward rectangle questions on Foundation to composite shapes and sectors on Higher. Knowing the formulas is not enough; you also need to identify which
§Key definitions
Step 1:
Write the formula: A = ½(a + b) × h.
Step 2:
Substitute: A = ½(8 + 12) × 5 = ½ × 20 × 5 = 50 cm².
Step 3:
Area of the L-shape = 80 − 12 = 68 m².
§Formulas to memorise
A = l \times w
A = \frac{1}{2} \times b \times h
A = b \times h
A = \frac{1}{2}(a + b) \times h
A = \pi r^2
A = \frac{\theta}{360} \times \pi r^2
A = \frac{1}{2} \times d_1 \times d_2
A = \frac{120}{360} \times \pi \times 6^2 = \frac{1}{3} \times 36\pi = 12\pi = \textbf{37.7 cm}^2 \text{ (1 d.p.)}
Worked example
See example below.
A trapezium has parallel sides of 8 cm and 12 cm and a perpendicular height of 5 cm. Find its area.
⚠ Common mistakes
- ✗Using the slant height instead of the perpendicular height. For triangles, parallelograms and trapeziums, you must use the height that is at right angles to the base.
- ✗Forgetting to halve. The triangle and trapezium formulas both include ½ — missing this doubles your answer.
- ✗Using diameter instead of radius for circles. The formula uses r, not d. If given the diameter, halve it first.
- ✗Not squaring the radius. Students sometimes calculate π × r instead of π × r².
- ✗Missing square units. Area must always be in cm², m², etc. — not cm or m.
✦ Exam tips
- →Write the formula before substituting — examiners award marks for stating the formula even if the arithmetic is wrong.
- →For composite shapes, sketch the breakdown and label each part. This helps you stay organised and avoids missing a section.
- →Leave answers in terms of π when asked. If the question says "give your answer in terms of π", do not use 3.14159 — write 12π.
- →Read the question for rounding instructions. "Give your answer to 3 significant figures" or "to 1 decimal place" tells you exactly what to do.
- →Check your answer by estimation. A circle with radius 5 cm should have an area of roughly 75–80 cm² (since π × 25 ≈ 78.5). If your answer is 785, you have likely used the diameter.