Area Outside Circle Inside Square

Hard Problem Solving Geometry

In a square, each vertex is located at one of the coordinates: (0, 0), (a, 0), (a, a), and (0, a), where a is the length of each side of the square.

A circle is inscribed within this square. What is the area of the region that is outside of the circle but inside the square?

$\left(\frac{\pi a^2}{4}\right)$

$\left(a^2 - \pi \left(\frac{a}{2}\right)^2\right)$

$\left(\frac{\pi a^2}{2}\right)$

$\left(a^2 - \frac{\pi a^2}{4}\right)$

Submitted3.6K

Correct2.1K

% Correct59%