Theory question 105
Mensuration of Plane ShapesA trapezium PQRS is such that PQ//RS and the perpendicular from P to RS is 40 cm. If |PQ| = 20cm, |SP| = 50 cm and |SR| = 60 cm, calculate, correct to 2 significant figures, the: (a) area of the trapezium; (b) ∠QRS.
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Model answer
(a) Area = ½(20 + 60) × 40 = 1600 cm² ≈ 1.6 × 10³ cm²
(b) Let the perpendicular from P meet SR at N: SN = √(50² − 40²) = 30 cm
The perpendicular from Q meets SR at M with SM = 30 + 20 = 50 cm, so MR = 60 − 50 = 10 cm
tan∠QRS = 40/10 = 4 → ∠QRS ≈ 76°
Explanation
Drop perpendiculars from P and Q to SR and use right-angled triangles.