# WAEC standard for Answering Shapes and Angles.

(a) In the diagram, *PQST* is a parallelogram, *PR* is a straight line,

│*TS*│ = 8 *cm*, │*SM*│= 6 *cm* and area of triangle *PSR *= 36 *cm*².

Find the value of │*QR*│.

(b) A tree and a flagpole are
on the same horizontal ground. A bird on top of the tree

observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively.

If the tree is 10.65 *m* high, calculate, correct to 3 significant figures, the height of the flagpole.

This question was reported to be poorly attempted by majority of the candidates. According to the report, they were unable to get the correct diagram in part (b) and this affected their ability to obtain the correct answer. In part (a), candidates were expected to show that │TS│ = │PQ│ = 8cm (opposite sides of parallelogram TSQP). Also, area of triangle PSR = ½│PR│(│SM│).

This implied that 36 = ½(8+|QR|) × 6 = 3(8+│QR|). Therefore, │QR│ = 36/3 – 8 = 4cm. In part (b), candidates were expected to represent the giving information in a diagram such as:

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.