21. The diagram shows four semicircles, one with radius $2 \mathrm{~cm}$, touching the other three, which have radius $1 \mathrm{~cm}$.

What is the total area, in $\mathrm{cm}^{2}$, of the shaded regions?
A 1
B $\pi-2$
C $2 \pi-5$
D $\frac{3}{2}$
E $\frac{1}{2} \pi$
21. B In the diagram, $S R$ is the diameter of the upper small semicircle and $P$ and $Q$ are the centres of the two lower small semicircles. Note that the line $S R$ touches the two semicircles with centres $P$ and $Q$ at points $S$ and $R$ respectively.
So $\angle S R Q=\angle R S P=90^{\circ}$.
Also, $S R=P Q=2 \mathrm{~cm}$. Therefore $P Q R S$ is a rectangle.

The total unshaded area in the diagram is the rectangle plus a semicircle and two quarter circles, that is, the rectangle plus a circle. So, in $\mathrm{cm}^{2}$, it is $1 \times 2+\pi \times 1^{2}=2+\pi$.
So the total shaded area, in $\mathrm{cm}^{2}$, is $\frac{1}{2} \times \pi \times 2^{2}-(2+\pi)=2 \pi-(\pi+2)=\pi-2$.
Hence the required area, in $\mathrm{cm}^{2}$, is $\pi-2$.