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Geometry & Measures · Foundation & Higher

Area of triangles & quadrilaterals

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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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

  1. 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

  1. Area of outer rectangle = 8 × 6 = 48 cm²
  2. Area of cut section = 3 × 2 = 6 cm²
  3. 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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