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A rhombus has an area of . One of its diagonals is 30 cm. Find the length of the other diagonal.

Class 8MensurationMensuration
  • A8 cm
  • B16 cm
  • C4 cm
  • D32 cm

Step-by-Step Solution

240 = ½ × 30 × d → 15d = 240 → d = 16 cm. Trap 8 cm: forgetting the ½ and computing 240 ÷ 30. Trap 4 cm: dividing by 2 instead of multiplying (240 ÷ 60). Trap 32 cm: doubling the correct answer, as if the ½ had to be undone at the end.
Answer: B) 16 cm

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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