The area of a square inscribed in a circle of diameter p cm is:

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\frac{p^{2}}{6} c m^{2}

\frac{p^{2}}{2} c m^{2}

\frac{p^{2}}{5} c m^{2}

\frac{p^{2}}{4} c m^{2}

answer is B.

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Detailed Solution

Given, the area of a square inscribed in a circle of diameter p cm.
Question Image

Diameter of the circle = p = Length of the diagonal of the square.
To find the area of a square.
Let us assume that the side of the square (ABCD) is a cm.
Now, using Pythagoras theorem in right

Δ A B C

{(AC)}^{2} = {(AB)}^{2} + {(BC)}^{2}

p^{2} = 2 a^{2}

a = \frac{p}{\sqrt 2}

Now,
Area of square =

sid e^{2}

Area of square = {(\frac{p}{\sqrt{2}})}^{2}

Thus, the area of the square is

\frac{p^{2}}{2} c m^{2}

.
Hence, option 2 is correct.

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