Question 5
A trapezium PQRS is such that PQ//RS and the perpendicular from P to RS is 40 cm. If |PQ| = 20 cm, |SP| = 50 cm and |SR| = 60 cm, calculate, correct to 2 significant figures, the:
- (a) area of the trapezium;
- (b) ÐQRS.
Observation
The Chief Examiner reported that the candidates who attempted this question and got it right were those who represented the given information in a diagram.
P
Q
20 cm
40 cm
In part (a), candidates were expected to recall the formula for calculating the area of a trapezium = 
(sum of parallel sides) × height = 
(20 + 60) × 40 = 1600 cm2. In part (b), candidates were expected to obtain the length MR first and then use it to calculate the required angle. |MR| = (60 - |NM| - |SN|) = (60 – 20 – (
)) = (60 – 20 - 
)) = 10 cm. Therefore, angle QRS = tan-1(
) = 76o, correct to 2 significant figures.