WAEC Mathematics 2006 Question 11

Question 11

Mensuration of Plane Shapes

In the diagram, PQUV, PQTU, QRTU and QRST are parallelograms. |UV| = 4.8 cm and the perpendicular distance between PR and VS is 5 cm. Calculate the area of quadrilateral PRSV.

A.96 cm²
B.72 cm²
C.60 cm²
D.24 cm²

Show the answer and explanation

Answer: C (60 cm²)

Explanation

Opposite sides of parallelograms are equal, so PQ = QR = 4.8 cm and VU = UT = TS = 4.8 cm. PRSV is a trapezium with parallel sides 9.6 cm and 14.4 cm: area = ½(9.6 + 14.4) × 5 = 60 cm².