Question

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

Answer 1

≡QUESTION≡

Find the area of the square that can be inscribed in a circle of radius 8 centimeter.

                                                     

║⊕ANSWER⊕║

Given, radius of circle (r) = 8 cm

Diameter of circle = 2 r

                               = 2 × 8

                               = 16 cm

Since, the square is inscribed in a circle,

then diameter of the circle will be equal to diagonal of the square.

Diagonals of a square

= √2 × side

diameter of circle = diagonal of square

16 cm = √2 × side

side = (16/√2 )

        = (16 /√2 ) × (√2 /√2 )

        = 16√2/ 2

        = 8√2 cm

Area of square = side × side

                          = 8√2 × 8√2

                          = 128 cm²

∴ Area of square = 128 cm²