Question

In the adjoining figure ABCD. P and R are the mid-points of the sides AB and CD. ABCD is a
parallelogram. What is the ratio of the shaded to the unshaded region ?
R
(1) 1/2
(2) 1/3
(3) 1/4
(4) none of these​

Answer 1

The correct answer is option (2) 1/3

GIVEN

ABCD is a parallelogram. P and R are the mid-points of the sides AB and CD.

TO FIND

What is the ratio of the shaded to the unshaded region?

SOLUTION

We can simply solve the above problem as follows;

If we join point P and Q. Extend the point S to T and Q to point U.

Join R to P.

The total number traingles = 16.

All 16 traingles are similar traingles.

Now,

Number of triangles in the shaded region = 4

Number of triangles in unshaded region = 16-4 = 12

Ration of Area of shaded region to unshaded region = 4/12 = 1/3

Hence, The correct answer is option (2) 1/3

Picture for reference.

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