WAEC Mathematics 2021 Theory — Question 15
Question 15 of 22 from the West African Examinations Council (WAEC) Mathematics 2021 Theory paper, with the correct answer and a full explanation.
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9. In the diagram, PQRS is a trapezium with QR∥PS. U and T are points on PS such that |PU|=5 cm, |QU|=12 cm and ∠PUQ=∠STR=90°. If the area of ΔPQR=20 cm², calculate, correct to the nearest whole number, the: (a) perimeter; (b) area of the trapezium.
Model answer
From area of ΔPQR = ½×QR×12 = 20, QR = 3.33 cm. By Pythagoras in ΔPUQ: |PQ|=√(12²+5²)=13 cm. Using the 50° angle at T with RT: |RS|=12/sin50°≈15.66 cm and |TS|=12/tan50°≈10.07 cm, so |PS|=|PU|+|UT|+|TS|=5+3.33+10.07≈18.4 cm. (a) Perimeter ≈ 13+3.33+15.66+18.4 ≈ 50 cm (nearest whole number). (b) Area of trapezium = ½(QR+PS)×12 = ½(3.33+18.4)×12 ≈ 130 cm².
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