Question

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

(i) area (PQRS) $=$ area (ABRS)

(ii) area (AXS) $=\frac{1}{2}$ area (PQRS)

Answer 1

(i) It can be observed that parallelogram PQRS and ABRS lie on the same base SR

and also, these lie in between the same parallel lines SR and PB.

∴ Area (PQRS) = Area (ABRS) ... (1)

(ii) Consider ΔAXS and parallelogram ABRS.

As these lie on the same base and are between the same parallel lines AS and BR,

∴ Area (ΔAXS) = $\frac{1}{2}$ Area (ABRS) ... (2)

From equations (1) and (2), we obtain

Area (ΔAXS) = $\frac{1}{2}$ Area (PQRS)