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  • Write true or false and justify your answer. In Fig., ABCD and EFGD are two parallelograms and G is the mid-point of CD. Then ar (DPC) = 1/2  ar ( EFGD).

Write true or false and justify your answer.
In Fig., ABCD and EFGD are two parallelograms and G is the mid-point of CD. Then ar (DPC) = \frac{1}{2} ar ( EFGD).

Answers (1)

best_answer

Answer: [False]

Solution.

Given that ABCD and EFGD are two parallelogram and G is mid-point of CD.
Let perpendicular distance between AB and CD be h
ar (\parallel gm) = (base) (corresponding altitude)
ar (\parallel EFGD) = (GD) (h)
ar (\parallel ABCD) = (CD) (h)
CD = 2 GD (Given that G is mid-point of CD)
So,  ar (\parallel ABCD) = 2 ar (\parallel EFGD)
\ ar (\parallel EFGD) = \frac{1}{2} ar (\parallel ABCD)          ....(i)
Now, DPDC and parallelogram ABCD are on the same base BC and between the same parallels AB and CD
So, ar (\triangle DPC) = \frac{1}{2} ar (\parallel ABCD) …(ii)
From (i) and (ii)

\Rightarrow ar (\triangle DPC) = ar (\parallel EFGD)

Therefore the given statement is false.

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infoexpert26

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