Question

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

Answer 1

Given that the radius of circle is 8cm.


Hence diameter would be 8×2 = 16 cm

Now, since the square is inscribed in the circle, the diameter would be the diagonal of the square.

Let the sides of square be a

So diagonal (By Pythagoras Theorem)

= √(a² + a² )

= √(2a²)

= a√2

Given that the diagonal = 16 cm

Hence, a√2 = 16 cm

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


So, side = 8√2

Hence, area = a² = (8√2)²

= 8² × (√2)²

= 64 × 2

= 128 cm²

Alternative method :-


Diameter = 16 cm

=> Diagonal = 16 cm

Area of a square is also given as :-

1/2 × diagonal × diagonal

=> 1/2 × 16 × 16

= 256 × 1/2

= 128 cm²


You may follow any one method
Hope it helps dear friend ☺️✌️

Answer 2

Given,

Radius of circle = 8cm

Then,

Diameter of Circle= 2 x r = (2 x 8) cm = 16 cm

Now,

As per your question, If Diameter of circle is equal to the diagonal of Square.

=> Diameter of Circle = Diagonal of Square = 16 cm

=> Diagonal of Square = 16 cm

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

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

Now,

Area of Square = a^2

$= > area \: = {( \frac{16}{ \sqrt{2} }) }^{2}$

$= > \: area \: = \frac{256}{2} \: \: {cm}^{2}$

$= > \: area \: \: = 128 \: {cm}^{2}$



Be Brainly