You need to find areas of triangles, rectangles, parallelograms, rhombuses and kites using appropriate formulas. Compound shapes can be split into simpler components.
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Revising area of triangles & quadrilaterals the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Area of triangles & quadrilaterals GCSE” on the site for the complete guide.
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Key facts to remember
1Area of a triangle = ½ × base × perpendicular height.
2Area of a rhombus or kite = ½ × d₁ × d₂ (product of diagonals ÷ 2).
3For compound shapes: split into rectangles and triangles, find each area, then add (or subtract).
4Always use the perpendicular height, not the slant side.
5Area is always measured in square units.
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Formulas
Triangle area
A = ½ × b × h
h is perpendicular height
Kite/Rhombus area
A = ½ × d₁ × d₂
d₁, d₂ are diagonals
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Worked examples
Example 1
Find the area of a triangle with base 10 cm and perpendicular height 7 cm.
Working
A = ½ × 10 × 7 = ½ × 70 = 35 cm²
Answer35 cm²
Example 2
Find the area of an L-shaped compound shape: outer rectangle 8 × 6 cm, with a 3 × 2 cm rectangle cut from one corner.
Working
Area of outer rectangle = 8 × 6 = 48 cm²
Area of cut section = 3 × 2 = 6 cm²
Area of compound shape = 48 − 6 = 42 cm²
Answer42 cm²
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Common mistakes
✗Using the slant height of a triangle instead of the perpendicular height.
✗Adding areas instead of subtracting when finding the area of a shape with a piece removed.
✗Forgetting the ½ in the triangle area formula.
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Exam tips
✓Draw a diagram and mark the perpendicular height clearly before calculating.
✓For compound shapes, draw lines to split them into rectangles and triangles and work out each part.
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