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Question -

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

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

(ii)ar (AXS) = ar (PQRS)



Answer -

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

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

Area (PQRS) = Area (ABRS) … (1)

(ii) Consider ΔAXS andparallelogram ABRS.

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

Area (ΔAXS) = Area (ABRS) … (2)

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

Area(ΔAXS) = Area (PQRS)

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