10,11 The sides of the base of a right parallelepiped are equal to $a$ and $b$ and form an angle of $30^{\circ}$. The lateral surface area is $S$. Find the volume of the parallelepiped.
Let $h$ be the height of the parallelepiped, $V$ be its volume, and $s$ be the area of the base. According to the problem,

$$
S=2 a h+2 b h=2 h(a+b),
$$

from which we find that $h=\frac{S}{2(a+b)}$. Therefore,

$$
V=s h=a b \sin 30^{\circ} \cdot h=\frac{1}{2} a b \cdot \frac{S}{2(a+b)}=\frac{\text { aS }}{4(a+b)} .
$$

## Answer