WAEC Mathematics 2021 Theory question 109

Theory question 109

Mensuration of Plane Shapes

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.

Show the model answer

Model answer

Area ΔPQR = ½ × |QR| × 12 = 20 → |QR| = 10/3 ≈ 3.33 cm
|PQ| = √(5² + 12²) = 13 cm; |RT| = 12 cm and ∠RST = 50° (from the diagram)
|RS| = 12/sin 50° ≈ 15.66 cm; |TS| = 12/tan 50° ≈ 10.07 cm
|PS| = 5 + 3.33 + 10.07 ≈ 18.40 cm
(a) Perimeter = 13 + 3.33 + 15.66 + 18.40 ≈ 50 cm
(b) Area = ½(3.33 + 18.40) × 12 ≈ 130 cm²

Explanation

The height of ΔPQR on base QR is the same 12 cm as the trapezium's height.