Question

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

Answer 1

Answer:

128 cm²

Step-by-step explanation:

Let ABCD is a square inscribed in a circle with centre O, where Radius of the circle is 8 cm

From the given figure, you can observe that  the diagonal of square inscribed in a circle is equal to diameter of the circle.

Diagonal of Square(AC)  = Diameter of Circle

                                = 2×8              [Diameter = 2(Radius)]

                          AC = 16 cm

In ΔABC

AB² + BC² = AC²          [By Pythagoras Theorem]

AB² + AB² = 16²         [AB = AC, sides of square are equal]

2AB² = 256

AB² = 128

∴ Side² = 128                [Side² = Area of Square]    

Hence Area of Desired Square is 128 cm²    

Answer 2

Hey there!

Given,

Radius of circle = 8 cm

Diameter = 2 * r = 16 cm

Here, The diameter of circle = diagonal of square = 16 cm

Then, Area of square = diagonal^2/2

                                  = 16^2/2

                                  = 256/2

                                  = 128 cm²

Good day!