A regular

A regular triangular prism with a base edge of 20 dm and a height of 30 dm is drawn. Find the volume of the prism and the area of the shell.

Correct answer:

V =  5196.1524 dm³
S =  1800 dm²

Step-by-step explanation:

$$\begin{gathered} a=20\text{dm} \\ h=30\text{dm} \\ {S}_1=a^2\cdot \frac{\sqrt{3}}{4}=20^2\cdot \frac{\sqrt{3}}{4}=100\sqrt{3}{\text{dm}}^2\doteq 173.2051{\text{dm}}^2 \\ V=S_1\cdot h=173.2051\cdot 30=3000\sqrt{3}=5196.1524{\text{dm}}^3 \end{gathered}$$

$S=3\cdot a\cdot h=3\cdot 20\cdot 30=1800{\text{dm}}^2$

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