Theory question 109
Mensuration of Plane ShapesIn the diagram, |PT| = 4 cm, |TS| = 6 cm |PQ| = 6 cm and ∠SPR = 30°. Calculate, correct to the nearest whole number: (a) |SR|; (b) area of TQRS.
Show the model answer
Model answer
TQ//SR, so triangles PTQ and PSR are similar: |PS| = 10 cm and |PR| = 6 × 10/4 = 15 cm
(a) |SR|² = 10² + 15² − 2 × 10 × 15 cos 30° ≈ 65.19 → |SR| ≈ 8.07 ≈ 8 cm
(b) Area PSR = ½ × 10 × 15 × sin 30° = 37.5 cm²
Area PTQ = ½ × 4 × 6 × sin 30° = 6 cm²
Area TQRS = 37.5 − 6 = 31.5 ≈ 32 cm²
Explanation
Find |PR| from similar triangles, then use the cosine rule.