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A field is a quadrilateral ABCD. The diagonal AC is 24 m long, and the perpendiculars dropped onto AC from the opposite corners B and D measure 8 m and 13 m. Find the area of the field.

Class 8MensurationMensuration
  • A
  • B
  • C
  • D

Step-by-Step Solution

Split along the diagonal: area = ½ × diagonal × (sum of the two perpendiculars) = ½ × = ½ × . Trap : forgetting the ½. Trap : using only one perpendicular (½ × ) and losing triangle ACD. Trap : reporting the sum of the perpendiculars, which is a length, not an area.
Answer: D)

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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