10.121. Calculate the area of a rectangular trapezoid if its acute angle is $60^{\circ}$, the smaller base is $a$, and the larger lateral side is $b$.
Solution.

The height of the trapezoid is $\frac{b \sqrt{3}}{2}$, and the larger base is $a+\frac{b}{2}$.

Therefore, its area $S=\frac{1}{2}\left(a+a+\frac{b}{2}\right) \frac{b \sqrt{3}}{2}=\frac{(4 a+b) b \sqrt{3}}{8}$.

Answer: $(4 a+b) b \sqrt{3} / 8$.