$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.$

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.

35cm²

65cm²

70cm²

140cm²

View answer & explanation

Correct answer is C

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 = 70cm $^2$

ALTERNATIVE METHOD

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

= 70cm $^2$

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