Question

In the given figure, PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal Q is joined. The ratio ar (||^gm XQRY) : ar (ΔQSR) =

(i) 1 : 4

(ii) 2 : 1

(iii) 1 : 2

(iv) 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)

(since X is the mid point of PQ and Y is the midpoint of SR)

Hence the correct answer is option (d).