IKMC 2010 - Grades 11-12 - Paper 02 - Self-study Question 10

Question 10

The square has side 2. The semicircles have their centres at the square’s vertices and pass through its centre. Each shaded circle has its centre on a side and is tangent to the adjacent semicircles. What is the total shaded area?

Question illustration

$4(3-2\sqrt2)\pi$
$\sqrt2\pi$
$\frac{\sqrt3}{4}\pi$
$\pi$
$\frac14\pi$