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If area of the parallelogram $ABCD$ is $92.4 cm$ . If $E$ and $F$ are the mid-points of $AB$ and $CD$ respectively, then area of parallelogram AEFD is:

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92.4 cm 2

46.2 cm 2

46.7 cm 2

184.8 cm 2

answer is B.

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Detailed Solution

Given that area of the parallelogram

ABCD

92.4 cm

and

E

and

F

are the mid-points of

AB

and

CD

respectively.
Question Image

We know that if the dimensions of parallelograms are same, then the area of those parallelogram are same.

A B = D C [Opposite sides of a parallelogram] ⇒ 12 A B = 12 D C [Dividing both sides by 2]

∴ A E = D F, E B = F C A E ∥ D F, E B ∥ F C

Thus, AEDF and EBCF are parallelograms.
And because their dimensions are same.

⇒ a r A E F D = a r E B C F ⇒ a r A E F D + a r E B C F = a r A B C D [From the figure] ⇒ a r A E F D = 12 92.4 [Given] ⇒ a r A E F D = 46.2 c m 2

Thus, the area is

46.2 c m 2

.
Hence, the correct option is 2.

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