Question

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

Answer 1

Dora !!!

radius = 8cm
diameter = 2*8 = 16cm

the square is inscribed in circle
diameter of circle = diagonal of square

(digonal)^2 = (side)^2 + (side)^2
(16)^2 = 2 (side)^2
256 = 2 (side)^2
256/2 = (side)^2
128 = (side)^2

Area of square = side*side
= (side)^2 = 128 cm sq.

Answer 2

$\large \bold{ \underline{ \underline{ \: \sf Answer : \: \: \: }}}$

$\to$ 128 cm²

$\large \bold{ \underline{ \underline{ \: \sf Explaination : \: \: \: }}}$

Given ,

$\star$ Radius of circle = 8 cm

$\star$ Diameter = 8 × 2 = 16 cm

Here ,

Diameter of circle = Diagonal of square

$\large \fbox{ \fbox{ \bold{ \sf \: Area \: of \: square = \frac{ {( \: Diagonal \: )}^{2} }{2} \: }}}$

$\to \sf Area \: of \: square = \frac{ {(16)}^{2} }{2} \\ \\\to \sf Area \: of \: square = \frac{256}{2} \\ \\\to \sf Area \: of \: square = 128 \: \: {cm}^{2}$

Thus , the required value is 128 cm²