2. B If the semicircle is cut into two quarter-circles, these can be placed next to the other shaded region to fill up half the square. Hence the shaded area is half of the area of the square, namely $\frac{1}{2} a^{2}$.
2. The diagram shows a square with sides of length $a$. The shaded part of the square is bounded by a semicircle and two quarter-circle arcs. What is the shaded area?
A $\frac{\pi a^{2}}{8}$
B $\frac{a^{2}}{2}$
C $\frac{\pi a^{2}}{2}$
D $\frac{a^{2}}{4}$
$\mathrm{E} \frac{\pi a^{2}}{4}$