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Question

In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that .
ar(ΔAXS)=12ar(PQRS) 


Solution

Consider parallelogram PQRS and parallelogram ABRS.
As these lie on the same base SR and are between the same parallel lines PB and SR,
ar(PQRS) = ar(ABRS) .....(1)

 Consider ΔAXS and parallelogram ABRS.
As these lie on the same base AS and are between the same parallel lines AS and BR,
ar(ΔAXS)=12ar(ABRS)...(2)

From equations(1) and(2), we obtain
ar(ΔAXS)=12ar(PQRS)
 

Mathematics
DUMMY
Standard IX

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