The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD

Question

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

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Accepted Answer

30. We are given that : Let DP =x So AB =x Now DP=CP So CD = 2x Now let height of trapezium be h we can say A(Parallelogram ABPD ) = xh And A (BPC) = 1 2 x h \frac{1}{2}xh 2 1 ​ x h Now by condition x h − 1 2 x h = 10 xh-\frac{1}{2}xh=10 x h − 2 1 ​ x h = 10 x h 2 = 10 \frac{xh}{2}=10 2 x h ​ = 10 so xh