11.060. The base area $P$ and volume $V$ of a regular quadrilateral prism are known. Calculate its total surface area.
Solution.

$S_{\pi}=2 S_{\text {base }}+4 S_{6 \text { side }}$ (Fig. 11.55), where $P=S_{\text {base }}$ and $P=a^{2}(a-$ side of the square). $V=P \cdot H \Rightarrow H=\frac{V}{P}$;

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-686.jpg?height=390&width=516&top_left_y=925&top_left_x=716)

Fig. 11.55 $S_{\text {side }}=a \cdot H=\sqrt{P} \cdot \frac{V}{P} \cdot$ Therefore,

$S=2 P+4 V \frac{\sqrt{P}}{P}$.

Answer: $\quad 2 P+\frac{4 V}{\sqrt{P}}$.