ABCD is a rectangle, ABEF is a parallelogram with area of 40 cm2 and AB and CF are parallel. Find area of rectangle ABCD.

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ABCD is a rectangle, ABEF is a parallelogram with area of $40 c m^{2}$ and $A B$ and $C F$ are parallel. Find area of rectangle ABCD.

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$30 c m^{2}$

$50 c m^{2}$

$40 c m^{2}$

$35 c m^{2}$

answer is C.

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Detailed Solution

Concept: It is known that if two parallelograms have the same base and lie between the same parallels, their areas are equal.

A rectangle can be considered as a special case of parallelogram.

Here, ABCD is a rectangle and ABEF is a parallelogram with area of $40 c m^{2}$ . $A B$ and $C F$ are parallel.

In the figure, we can see that ABCD and ABEF lie on the same base and between the same parallels.

Therefore,

$A r e a (A B C D) = A r e a (A B E F) = 40 c m^{2}$

Hence, the area of rectangle ABCD is $40 c m^{2}$ .

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