15. (15 points) As shown in the figure, two right-angled triangles, Jia and Yi, are cut from a parallelogram paper. The two legs of the right-angled triangle Jia are $8 \mathrm{~cm}$ and $5 \mathrm{~cm}$. The two legs of the right-angled triangle Yi are $6 \mathrm{~cm}$ and $2 \mathrm{~cm}$. Find the area of the shaded part in the figure.
【Solution】Solution: According to the analysis, as shown in the figure, the areas of $\triangle A E B$, $\triangle A B H$, and $\triangle C D M$ are equal, and the areas of $\triangle B C N$, $\triangle B C P$, and $\triangle A F D$ are equal. From the figure, we can see that,
the area of the shaded part $=$ the area of rectangle $E N M F - \triangle A E B - \triangle A B H - \triangle C D M - \triangle B C N - \triangle B C P - \triangle A F D$
$=$ the area of rectangle $E N M F - 3 \times (S_{\text {Jia }} + S_{\text {Yi }})$;
From the figure, we can see that the length of rectangle $E N M F = 6 + 8 = 14 \mathrm{~cm}$, and the width $= 5 + 2 = 7 \mathrm{~cm}$,
so the area of rectangle $E N M F = 14 \times 7 = 98 \mathrm{~cm}^{2}$, and the area of the shaded part $= 98 - 3 \times \frac{1}{2} \times (5 \times 8 + 6 \times 2)$ $= 20 \mathrm{~cm}^{2}$.
Therefore, the answer is: 20.
15. (15 points) As shown in the figure, two right-angled triangles, Jia and Yi, are cut from a parallelogram paper. The two legs of the right-angled triangle Jia are $8 \mathrm{~cm}$ and $5 \mathrm{~cm}$. The two legs of the right-angled triangle Yi are $6 \mathrm{~cm}$ and $2 \mathrm{~cm}$. Find the area of the shaded part in the figure.