Question

4(a). In the diagram above, PQRS is a quadrilateral, ∠PQR = ∠PRS = 90°, |PQ| = 3cm, |QR| = 4cm and |PS| = 13cm. Find the area of the quadrilateral.

Accepted Answer

Area of quadrilateral PQRS = area of ΔPQR + area of ΔRPS.
By Pythagoras' theorem in ΔPQR: PR² = PQ²+QR² = 3²+4² = 9+16 = 25 ⇒ |PR| = 5cm.
Similarly, in ΔRPS: PS² = RS²+PR² ⇒ 13² = RS²+5² ⇒ 169−25 = RS² ⇒ RS²=144 ⇒ |RS| = 12cm.
Area = ½×4×3 + ½×12×5 = 6 + 30 = 36 cm².

WAEC Mathematics 2019 Theory — Question 5

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