Task B-1.3. One leg of the trapezoid is $16 \mathrm{~cm}$ long and forms an angle of $30^{\circ}$ with the base. The other leg forms an angle of $45^{\circ}$ with the base. Calculate the area of the trapezoid if the shorter base is $2 \mathrm{~cm}$ long.
Solution. complete sketch (with all triangles)

(1 point)

![](https://cdn.mathpix.com/cropped/2024_05_30_247a158c2fc9e6452974g-02.jpg?height=509&width=1439&top_left_y=575&top_left_x=300)

$$
\begin{gathered}
v=8 \mathrm{~cm} \\
a=8 \sqrt{3}+2+8 \mathrm{~cm} \\
P=\frac{a+c}{2} \cdot v=32 \sqrt{3}+48 \mathrm{~cm}^{2}
\end{gathered}
$$