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In the figure, PQST is a parallelogram and TSR is a straight line. If the area o...


Question

In the figure, PQST is a parallelogram and TSR is a straight line. If the area of \(\bigtriangleup\)QRS is 20cm2, find the area of the trapezium PQRT.

Options

A) 35cm2

B) 65cm2

C) 70cm2

D) 140cm2

The correct answer is C.

Explanation:

A\(\bigtriangleup\) = \(\frac{1}{2}\) x 8 x h = 20

= \(\frac{1}{2}\) x 8 x h = 4h

h = \(\frac{20}{4}\)

= 5cm

A\(\bigtriangleup\)(PQTS) = L x H

A\(\bigtriangleup\)PQRT = A\(\bigtriangleup\)QSR + A\(\bigtriangleup\)PQTS

20 + 50 = 70cm2

ALTERNATIVE METHOD

A\(\bigtriangleup\)PQRT = \(\frac{1}{2}\) x 5 x 28

= 70cm2


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Dicussion (1)

  • A\(\bigtriangleup\) = \(\frac{1}{2}\) x 8 x h = 20

    = \(\frac{1}{2}\) x 8 x h = 4h

    h = \(\frac{20}{4}\)

    = 5cm

    A\(\bigtriangleup\)(PQTS) = L x H

    A\(\bigtriangleup\)PQRT = A\(\bigtriangleup\)QSR + A\(\bigtriangleup\)PQTS

    20 + 50 = 70cm2

    ALTERNATIVE METHOD

    A\(\bigtriangleup\)PQRT = \(\frac{1}{2}\) x 5 x 28

    = 70cm2

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