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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) =┬аar (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.

тИ┤Area (PQRS) = Area (ABRS) тАж (1)

(ii) Consider ╬ФAXS andparallelogram ABRS.

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

тИ┤ Area (╬ФAXS) =┬аArea (ABRS) тАж (2)

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

Area(╬ФAXS) =┬аArea (PQRS)

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