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Question
In the given figure, PQRS is a parallelogram. If X and Y are mid-points of PQ and SRrespectively and diagonal Q is joined. The ratio ar (||gm XQRY) : ar (ΔQSR) =
Options
1 : 4
2 : 1
1 : 2
1 : 1
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Solution
Given: (1) PQRS is a parallelogram.
(2) X is the midpoint of PQ.
(3) Y is the midpoint of SR.
(4) SQ is the diagonal.
To find: Ratio of area of ||gm XQRY : area of ΔQRS.
Calculation: We know that the triangle and parallelogram on the same base and between the same parallels are equal in area.
∴ Ar (||gm PQRS) = Ar (ΔQRS)
`Ar ( "||"^(gm) XQRY ) = 1/2 Ar ("||"^(gm) PQRS)`
(since X is the mid point of PQ and Y is the midpoint of SR)
`Ar ("||"^(gm) XQRY) = Ar (ΔQRS)`
`Ar ("||"^(gm) XQRY ) : Ar (ΔQRS) = 1:1`
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