Question

In a given figure, ABCD is a parallelogram, P and Q are the mid points of sides CD and BC respectively. Then the ratio of area of shaded portion: area of unshaded portion is

A 5 : 3 Correct Answer Incorrect Answer
B 3 : 5 Correct Answer Incorrect Answer
C 2 : 1 Correct Answer Incorrect Answer
D 3 : 1 Correct Answer Incorrect Answer

Solution

Let the total area of parallelogram = 32 units Area of parallelogram AXPD = 32/2 = 16 units Area of ∆APD = 16/2 = 8 units Area of parallelogram ABQY = 32/2 = 16 units Area of ∆ABQ = 16/2 = 8 units Area of parallelogram AOCQ = 32/4 = 8 units Area of ∆PQC = 8/2 = 4 units Area of ∆PQA = 32 - 20 = 12 units ∴ Area of shaded portion : Area of unshaded portion = 20 : 12 ⇒ 5 : 3 

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