CLASS 8 MATHS · MENSURATION

Area of a trapezium and a quadrilateral

Trapezium area = ½ × (sum of parallel sides) × height. Quadrilateral = ½ × diagonal × (sum of perpendiculars to it).

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Worked examples

Example 1 · level 1

Ayaan's farm field near Kochi is a trapezium with parallel sides 14 m and 14 m. The distance between them is 2 m. Find its area in square metres.

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Area = ½ × (14 + 14) × 2
= ½ × 28 × 2 = 28 m².

Answer: 28

Example 2 · level 2

A quadrilateral plot has a diagonal of 29 m. The perpendiculars from the other two corners to this diagonal are 3 m and 7 m. Find its area in square metres.

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Area = ½ × 29 × (3 + 7)
= ½ × 29 × 10 = 145 m².

Answer: 145

Example 3 · level 3

A trapezium-shaped garden has area 202.5 m² and parallel sides 26 m and 19 m. What is the distance between the parallel sides (in m)?

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202.5 = ½ × 45 × h = 22.5 × h.
h = 202.5 ÷ 22.5 = 9 m.

Answer: 9 m