Question

Prove that “Rectangle ABCD and parallelogram XBCY are equal in the area standing on the same base BC, between same parallel lines AY.”

Answer 1

Given:

Rectangle ABCD and parallelogram XBCY are on the same base BC, between same parallel lines AY.

To prove:

The area of the rectangle and parallelogram are the same.

Proof:

As we know that the rectangle and parallelogram are on the same base and between same parallel lines and the height of the parallel line at every point is constant

Let the base of the rectangle is 'b' and height of the parallel lines is 'h',

The height of the parallel lines is nothing just the breadth of the rectangle

Area of the rectangle ABCD

Length × Breadth

you can write this as:

• Base × height
• bh

and the area of the parallelogram XBCY is

• Base × height
• bh

Area of the rectangle ABCD = Area of the parallelogram XBCY

Hence proved