Area of the parallelogram $\mathrm{ABCD}=60\mathrm{ }{\mathrm{cm}}^2$. From the figure, find the area of the parallelogram ABEF.
 

Given:
Parallelogram $\mathrm{ABCD} \mathrm{area}=60\mathrm{ }{\mathrm{cm}}^2$.  

In the given figure, we have,
$\mathrm{AB}\parallel \mathrm{EF}$

$\mathrm{AD}\parallel \mathrm{BC}$

$\mathrm{EF}\parallel \mathrm{AF}$

Now, two parallelograms have same area when they are on same base and located between same parallels. 

In our case both parallelograms have same area.

The area of the parallelogram ABEF = The area of parallelogram ABCD

The area of the parallelogram ABEF = $\mathbf{60}\mathbf{ }{\mathbf{cm}}^{\mathbf{2}}$.