In the diagram, PQUV, PQTU, QRTU and QRST are parallelograms. |UV| = 4.8cm and the...

WAEC 2006

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

A. 96cm²
B. 72cm²
C. 60cm²
D. 24cm²

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Correct Answer: Option C

Explanation

|VU| = |UT| = |TS|

|VS| = (4.8) x 3 = 14.4cm

|PQ| = |QR| = 4.8

|PR| = (4.8) x 2 = 9.6cm

Since quad. PRSV is a trapezium of height 5cm

Area of quad. PRSV = \(\frac{1}{2}(a + b)h\)

= \(\frac{1}{2}(14.4 + 9.6) \times 5\)

= \(\frac{1}{2}(24) \times 5\)

12 x 5 = 60cm²

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