2020 AMC 12B Question 11 - thichhoctoan.com

Question 11

As shown in the figure below, six semicircles lie in the interior of a regular hexagon with side length $2$ so that the diameters of the semicircles coincide with the sides of the hexagon. What is the area of the shaded region—inside the hexagon but outside all of the semicircles?

Question illustration

$6\sqrt{3} - 3\pi$
$\dfrac{9\sqrt{3}}{2} - 2\pi$
$\dfrac{3\sqrt{3}}{2} - \dfrac{\pi}{3}$
$3\sqrt{3} - \pi$
$\dfrac{9\sqrt{3}}{2} - \pi$