Question

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that area of ∆APB = area of ∆BQC.

Answer 1

Area of Area of ΔBQC = Area ΔAPB as both the triangles and parallelogram lie on the same line

Points = 2 = P and Q (Given)

Sides = 2 = DC and AD (Given)

Parallelogram = ABCD (Given)

║gram ABCD and Δ BQC are on the same line BC and between the same parallel lines AD and BC.

Therefore,

Area (ΔBQC) = 1/2 Area (ABCD) ---1

Similarly,

║gram ABCD and Δ APB  are on the same line AB and between the same parallel lines AB and DC.

Therefore,

Area (ΔAPB) = 1/2 Area (ABCD) -- 2

From both the equations 1 and 2 we will get -

Area of ΔBQC = Area ΔAPB