General Mathematics Paper 2, May/June. 2015

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.