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


Question

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.

Options

A) 96cm2

B) 72cm2

C) 60cm2

D) 24cm2

The correct answer is 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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Dicussion (1)

  • |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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