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

Answer 1

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`