Question

If a triangle and a parallelogram lie on the same base and between the same parallels, then prove that the area of the triangle is equal to half of the area of parallelogram

Answer 1

Let ΔAPB and parallelogram ABCD lie on base AB and between parallels AB and PC.

To show area ΔAPB = `1/2` Area (ABCD)

Now, draw BQ || AP.

Then ABQP is a parallelogram.

Now area ABQP = Area ABCD .....(They are on same base AB and between same parallels AB and PC)

⇒ ΔPAB ≅ ΔBQP

Area PAB = Area BQP

= `1/2` Area ABQP

= `1/2` Area ABCD