Find the sum of areas of POQ and ORS

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Question

Find the sum of areas of POQ and ORS

Options:

A .

\frac{p q}{2}

B .

\frac{p^{2} q^{2}}{2}

C .

\frac{p^{2} + q^{2}}{2}

D .

\frac{p^{2} + q^{2}}{8}

Answer: Option A
:
A

Since the only condition we need to maintain is that the diagonals need to intersect at right angles, assume the simplest quadrilateral which satisfies this condition- a square. Now the question can be solved by simple graphical division.

Take the side of the square =p=q=2. Area = 4.

We need the area of the shaded region, which is half of that of the square= 2. Look in the answer options for 2 on substituting p=2 and q=2. Answer is option (a)

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