Question

find the area of the square that can be incribed in a circle of radius 8 cm.

Answer 1

Since the square is inscribed in the circle

Diagonal of square = Diameter of circle
=> side * root 2 = 16
=> Side of square = 16/ (root 2)

Area of square = Side ^2
= 256/2
= 128 cm^2

Hope it will help you

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Answer 2

Hey mate..
========

Given,

Radius of a circle, r = 8cm

Diameter of a circle, d = ( r * 2) = ( 8 * 2) = 16cm

Let, the side of the square be a cm

We know,

Diagonal of a square =$\sqrt{2} a$

From the figure, it can be seen that,

Diagonal of a square = Diameter of the circle

=> $\sqrt{2a} = 16 \\ \\ = > a = \frac{16}{ \sqrt{2} } \\ \\ = > a = 8 \sqrt{2} \: cm$

We know,

Area of a square = $(side) {}^{2}$

= $(a) {}^{2} = (8 \sqrt{2} ) {}^{2} = 128 \: cm {}^{2}$

Hope it helps.!