Is it true to say that the area of a square i | vedclass

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(D) The statement is false.When a square is inscribed in a circle,the diagonal of the square is equal to the diameter of the circle.Let the side of th

Vedclass · Accepted Answer

No,because the area of the square is $\frac{1}{2} p^{2} \, cm^{2}$.

Vedclass · Answer

(D) The statement is false.When a square is inscribed in a circle,the diagonal of the square is equal to the diameter of the circle.Let the side of the square be $a$ and the diameter of the circle be $p$.According to the property of a square,the diagonal $d = a\sqrt{2}$.Since the diagonal equals the diameter,we have $a\sqrt{2} = p$,which implies $a = \frac{p}{\sqrt{2}}$.The area of the square is $a^{2} = (\frac{p}{\sqrt{2}})^{2} = \frac{p^{2}}{2} \, cm^{2}$.Therefore,the area is $\frac{1}{2} p^{2} \, cm^{2}$,not $p^{2} \, cm^{2}$.

Is it true to say that the area of a square inscribed in a circle of diameter $p \, cm$ is $p^{2} \, cm^{2}$? Why?

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