Question

A square ,with perimeter 16,is inscribed in a circle.what is the area of the circle?

Answer 1

Let side of square be 'a'

4a=16

a=4cm

Diagonal of square=√2a=4√2cm

As square is inscribed in the circle, diameter of circle becomes the diagonal of the square

Let radius of circle be x

2x=4√2

x=2√2

So area of circle=πx^2

=3.14×2√2×2√2

=25.12 cm^2