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 formula to use, pick out the correct measurements, and handle units properly. This guide covers every 2D area formula you need for GCSE, provides worked examples at both tiers, flags the mistakes examiners see most often, and gives you practice questions. For a complete formula reference, see our GCSE Maths formulas guide.

What Is Area?

Area is the amount of two-dimensional space a shape covers. It is measured in square units such as cm², m², or km².

Key Area Formulas

Rectangle: $$A = l \times w$$

Triangle: $$A = \frac{1}{2} \times b \times h$$ where b is the base and h is the perpendicular height.

Parallelogram: $$A = b \times h$$ where h is the perpendicular height, not the slant side.

Trapezium: $$A = \frac{1}{2}(a + b) \times h$$ where a and b are the two parallel sides and h is the perpendicular distance between them.

Circle: $$A = \pi r^2$$

Sector of a circle: $$A = \frac{\theta}{360} \times \pi r^2$$ where θ is the angle at the centre.

Kite: $$A = \frac{1}{2} \times d_1 \times d_2$$ where d₁ and d₂ are the diagonals.

Step-by-Step Method

1. Identify the shape. Is it a triangle, parallelogram, trapezium, circle, sector, or a composite shape?
2. Write the formula. This earns you a method mark.
3. Pick out the correct measurements. Be careful to use perpendicular heights, not slant lengths.
4. Substitute and calculate.
5. Give units. Always write cm², m², etc.
6. For composite shapes, split the shape into simpler shapes, find each area, then add (or subtract) as needed.

Worked Example 1 — Foundation Level

A trapezium has parallel sides of 8 cm and 12 cm and a perpendicular height of 5 cm. Find its area.

Step 1: Write the formula: A = ½(a + b) × h.

Step 2: Substitute: A = ½(8 + 12) × 5 = ½ × 20 × 5 = 50 cm².

Follow-up: Triangle

A triangle has a base of 9 cm and a perpendicular height of 6 cm.

A = ½ × 9 × 6 = 27 cm².

Worked Example 2 — Higher Level

The diagram shows an L-shaped room. The overall dimensions are 10 m by 8 m, with a 4 m by 3 m rectangle cut from one corner. Find the area of the room.

Step 1: Area of the full rectangle = 10 × 8 = 80 m².

Step 2: Area of the cut-out = 4 × 3 = 12 m².

Step 3: Area of the L-shape = 80 − 12 = 68 m².

Sector Example

Find the area of a sector with radius 6 cm and angle 120°.

$$A = \frac{120}{360} \times \pi \times 6^2 = \frac{1}{3} \times 36\pi = 12\pi = \textbf{37.7 cm}^2 \text{ (1 d.p.)}$$

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.
• Composite shapes — adding when you should subtract. If a piece is cut out, subtract its area. If shapes are joined, add.

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.

Practice Questions

Question 1 (Foundation) Find the area of a rectangle with length 7.5 cm and width 4 cm.

Question 2 (Foundation) A circle has a diameter of 10 cm. Find its area. Give your answer to 1 decimal place.

Question 3 (Higher) A trapezium has parallel sides of 6.2 cm and 9.8 cm and a perpendicular height of 4.5 cm. Find its area.

Question 4 (Higher) A shape is made from a rectangle (12 cm by 8 cm) with a semicircle removed from one of the shorter sides. Find the shaded area to 1 decimal place.

Question 5 (Higher) Find the area of a sector with radius 9 cm and angle 150°. Give your answer in terms of π.

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Related Topics

• Perimeter — the total distance around a 2D shape
• Volume of 3D Shapes — extends area into three dimensions
• Surface Area — uses 2D area formulas applied to faces of 3D shapes
• Circle Theorems — sectors and segments involve area of circles
• Unit Conversions — converting between cm² and m²

Summary

Area measures the two-dimensional space inside a shape and is always given in square units. You must memorise the formulas for rectangles, triangles, parallelograms, trapeziums, circles and sectors. Always use the perpendicular height, write the formula before substituting, and double-check whether you need to add or subtract areas in composite shape questions. State your answer with correct units and appropriate rounding. Area questions appear on every GCSE paper, so having these formulas at your fingertips is essential.