Question

5. A trapezium PQRS is such that PQ//RS and the perpendicular from P to RS is 40cm. If |PQ|=20cm, |SP|=50cm and |SR|=60cm, calculate to two significant figures: (a) the area of the trapezium; (b) ∠QRS.

Accepted Answer

(a) Area of trapezium = ½(PQ+SR)×height = ½(20+60)×40 = ½(80)(40) = 1600cm².
(b) Using Pythagoras in the right triangle formed: |SN|²=|PS|²−|PN|²=50²−40²=900, |SN|=30cm. |NR|=|SR|−|SN|=60−30=... following the full construction, |MR|=10cm and tanα=|QM|/|MR|=40/10=4, giving ∠QRS = tan⁻¹(4) ≈ 76° (2 s.f.).

WAEC Mathematics 2015 Theory — Question 9

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