362. In a trapezoid with acute angles at the base, the height and diagonals are given. Determine the sum of the bases of the trapezoid.

*363. Let $S A B C$ be a triangular pyramid, and $M$ be an arbitrary point taken inside the pyramid. Is it always true that

$$
M A+M B+M C<S A+S B+S C ?
$$
362. Let $A B C D$ be the given trapezoid (Fig. 41), $A C=a, B D=b, B A_{1}=h$. If we shift the diagonal $A C$ parallel to the direction $B C$ by the length $A A_{1}$, we will obtain a rectangular trapezoid $A_{1} B C_{1} D$. Obviously,

$$
A D+B C=A_{1} D+B C_{1}
$$

since when the diagonal $A C$ is shifted parallel, the bases of the trapezoid change, but their sum remains constant. From the right triangles $A_{1} B D$ and $A_{1} B C_{1}$, we find:

$$
\begin{aligned}
& A_{1} D=\sqrt{(B D)^{2}-\left(B A_{1}\right)^{2}}=\sqrt{b^{2}-h^{2}} \\
& B C_{1}=\sqrt{\left(A_{1} C_{1}\right)^{2}-\left(B A_{1}\right)^{2}}=\sqrt{a^{2}-h^{2}}
\end{aligned}
$$

Thus,

$$
A D+B C=A_{1} D+B C_{1}=\sqrt{a^{2}-h^{2}}+\sqrt{b^{2}-h^{2}}
$$