Question

A square is inscribed in a circle and a semi circle of same radius. Find ratio of other two squares

Answer 1

Let side of square be 'a'

Area of square is a²

Diagonal of sqare is √{a²+a²}

Or √2a

So diameter of circle is equal to diagonal of sqare.

Then diameter=√2a

Radius(r)=√2a/2

=a/√2

Area of circle=πr²

=π{a/√2}²

=πa²/2

Ratio of area of square and area of circle =

a²:πa²/2

=1:π/2

=2:π