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A quadrilateral plot has an area of . One of its diagonals is 30 m, and the perpendicular from one corner onto that diagonal is 12 m. Find the perpendicular from the opposite corner.

Class 8MensurationMensuration
  • A25 m
  • B0.5 m
  • C13 m
  • D12.5 m

Step-by-Step Solution

375 = ½ × 30 × (12 + h) = 15(12 + h) → 12 + h = 25 → h = 13 m. Trap 25 m: that is the SUM of the two perpendiculars — subtract 12. Trap 0.5 m: forgetting the ½ gives 30(12 + h) = 375, so 12 + h = 12.5. Trap 12.5 m: 375 ÷ 30, which skips the ½ and the subtraction.
Answer: C) 13 m

Key idea: Area of a trapezium

**Area of a trapezium = ½ × (sum of parallel sides) × height.**

The height is the **perpendicular distance** between the two parallel sides — NOT the slant length of the non-parallel side.

Example: parallel sides 8 cm and 5 cm, height 4 cm. Area = ½ × = ½ × .

Why ½? You can split a trapezium into a rectangle plus a triangle (or chop and rearrange into a rectangle of the average parallel side). The factor of ½ comes from averaging the two parallel sides.

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