Illustrate a semicircle with diameter $A G$. The arc of the semicircle is divided into six equal parts by points $B$, $C$, $D$, $E$, and $F$. $D F$ and $C G$ are both straight line segments. Given that the area of the semicircle is $60 \mathrm{~cm}^{2}$, what is the area of the shaded part in $\mathrm{cm}^{2}$?
Geometry, Circle and Sector.
Let the center of the semicircle be point $O$, and connect $O C, A C$;
Since $A O = C O$;
Therefore, $S_{\triangle A O C} = S_{\triangle C O G}$;
Since $S_{\text {sector } A B C} = S_{\text {sector } D E F}$;
Therefore, $S_{\text {shaded }} = S_{\text {semicircle }} - S_{\text {sector }} = S_{\text {semicircle }} - \frac{2}{3} S_{\text {semicircle }} = \frac{1}{3} S_{\text {semicircle }} = \frac{1}{3} \times 60 = 20$ square centimeters.