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Step-by-Step Solution
Area = ½ × = ½ × . The 10 cm is the SLANT side and must be ignored. Trap : using 10 cm as the height. Trap : forgetting the ½. Trap : multiplying the two parallel sides as if it were a rectangle.
Answer: C)
In trapezium PQRS, PQ ∥ SR with PQ = 20 cm and SR = 12 cm. The slanting side QR is 10 cm long, while the perpendicular distance between PQ and SR is 6 cm. Find the area of PQRS.
Class 8MensurationMensuration
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.
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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