State True/False:

The area of a parallelogram and a rectangle with the same base and parallels are the same.

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

In the adjoining figure, parallelogram ABCD and rectangle ABEF are on the same base BC and between the same parallels AB and CF.

Therefore, area of parallelogram ABCD = Base × Height

Therefore, area of parallelogram ABCD = = AB × AF  ...........(1)

Also, Area of rectangle ABEF = Length × Width

Therefore, Area of rectangle ABEF == AB × AF           ...........(2)                                                   

From equation (1) and (2), we get:

Area of parallelogram ABCD = Area of rectangle ABEF

Hence, the given statement is true.