ABCD is a rectangle, ABEF is a parallelogram with area of $40 c{m}^2$ and  $AB$ and  $CF$ are parallel. Find area of rectangle ABCD.

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  $40 c{m}^2$. $AB$ and $CF$ are parallel.

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

Therefore, 

$Area\left(ABCD\right)=Area\left(ABEF\right)=40 c{m}^2$

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