Theory question 112
Mensuration of Plane Shapes(a) The area of trapezium PQRS is 60 cm2. PQ//RS, |PQ| = 15 cm, |RS| = 25 cm and ∠PSR = 30°. Calculate the (i) perpendicular height of PQRS; (ii) |PS|.
(b) Ade received 3/5 of a sum of money, Nelly 1/3 of the remainder while Austin took the rest. If Austin's share is greater than Nelly's share by ₦3,000, how much did Ade receive?
Show the model answer
Model answer
(a)(i) 60 = ½(15 + 25) × h = 20h, so h = 3 cm.
(ii) sin 30° = h/|PS|, so |PS| = 3/0.5 = 6 cm.
(b) Let the sum be x. Remainder = 2x/5. Nelly = ⅓ × 2x/5 = 2x/15; Austin = 4x/15.
4x/15 − 2x/15 = 2x/15 = 3000, so x = ₦22,500.
Ade received 3/5 × 22,500 = ₦13,500.
Explanation
Express each share as a fraction of the whole sum.