Question

In figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:

(i) ar (PQRS) = ar (ABRS)

(ii) ar (AXS) = 1/2ar (PQRS)

Answer 1

(i) As we know that parallelograms on the same base and between the same parallels are equal in area.

Here parallelograms PQRS and ABRS are on the same base SR and between the same parallels PB and SR. Therefore,

ar (PQRS) = ar (ABRS)

(ii) Again ∆AXS and parallelogram ABRS are on the same base AS and between the same parallels AS and BR.

∴ ar (∆AXS) = \(\frac { 1 }{ 2 }\) ar (∆BRS)

But ar (ABRS) = ar (PQRS)

(proved earlier)

⇒ ar (AXS) = \(\frac { 1 }{ 2 }\) ar (PQRS)