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in Mathematics by (3.5k points)

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

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

(ii) ar (ΔPXS) = 1/2 ar (PQRS)

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(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) = 1/2 Area (ABRS) ... (2)

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

Area (ΔAXS) = 1/2 Area (PQRS)

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