Regular prism

The regular four-sided prism has a base of 25 cm² and a surface of 210 cm². Find its volume.

Correct answer:

V =  200 cm³

Step-by-step explanation:

$$\begin{gathered} S_1=25{\text{cm}}^2 \\ S=210{\text{cm}}^2 \\ a=\sqrt{S_1}=\sqrt{25}=5\text{ cm } \\ S=2\cdot S_1+4av \\ v=(S-2\cdot S_1)\mathrm{/}(4\cdot a)=(210-2\cdot 25)\mathrm{/}(4\cdot 5)=8\text{ cm } \\ V=S_1\cdot v=25\cdot 8=200{\text{cm}}^3 \end{gathered}$$

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