Question

A square is inscribed in a circle with radius 4 inches, how do you find the area of the region inside the circle and outside the square?

Answer 1

Answer:

Each side of the square is a chord of the circle, call it C.

The length of a diagonal of the square is 2 R.

Then C^2 + C^2 = (2 R)^2

2 C^2 = 4 R^2   and C = 2^1/2 R = 1.414 R

So the area of the circle is pi * R^2

The area of the square is C^2 = 2 R^2

And the area outside of the square is (pi - 2) * R^2