11.048. Find the volume of an oblique triangular prism, the base of which is an equilateral triangle with a side equal to $a$, if the lateral edge of the prism is equal to the side of the base and is inclined to the base plane at an angle of $60^{\circ}$.
## Solution.

Draw $A_{1} K$ perpendicular to the plane $A B C$ (Fig. 11.43); then $V=S_{\triangle A B C} \cdot A_{1} K$, where $S_{\triangle A B C}=\frac{a^{2} \sqrt{3}}{4}$. Considering that $\angle A_{1} A K=60^{\circ}$, we find $A_{1} K=\frac{a \sqrt{3}}{2}$. Therefore, $V=\frac{a^{2} \sqrt{3}}{4} \cdot \frac{a \sqrt{3}}{2}=\frac{3 a^{3}}{8}$.

Answer: $\frac{3 a^{3}}{8}$.