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  • Is it true to say that area of a square inscribed in a circle of diameter p cm is p square cm square? Why?

Is it true to say that the area of a square inscribed in a circle of diameter p cm is p2cm2? Why?

Answers (1)

False

In the figure, we see that the diameter of the circle is equal to the diagonal of a square

Hence, the diagonal of square = p cm

Let side of the square = a cm            Using Pythagoras' theorem we get

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

Area of square = side × side

 =\frac{p}{\sqrt{2}} \times \frac{p}{\sqrt{2}}=\frac{p^{2}}{2}cm^{2}

Here we found that the area of the square is not equal to p2cm2.                

Hence the given statement is False

           

Posted by

infoexpert24

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