Question

PQRS and ABRS are parallelograms and X is any point on the side BR. Show that
(i) ar(PQRS)=ar(ABRS)
(ii) ar(ΔAXS)=1/2ar(PQRS)

Answer 1

i ) Area( PQRS ) = Area( ABRS )

solution :

Parallelogram PQRS and

parallelogram ABRS are on same base

SR and between the same parallels

SR//PB.

Therefore ,

area(PQRS) = area( ABRS )-----( 1 )

ii ) Area( ∆AXS ) = ( 1/2 ) Area ( PQRS )

Solution :

From ( 1 ) ,

area ( PQRS ) = area ( ABRS )

and parallelogram ABRS and ∆AXS

are on the same base AS and between

the same parallels AS//BR .

Therefore ,

∆AXS = ( 1/2 ) area ( ABRS )

= ( 1/2 ) Area ( PQRS ) [ from ( 1 ) ]

Hence proved .

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