The regular

The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.

Correct result:

V =  489.1941 cm³

Solution:

$$\begin{gathered} a=86\text{ mm}\to \text{ cm}=86\mathrm{/}10\text{ cm}=8.6\text{ cm } \\ r=6.4\text{ cm } \\ h=24\text{ cm } \\ {h}_1=\sqrt{r^2-(a\mathrm{/}2{)}^2}=\sqrt{6.4^2-(8.6\mathrm{/}2{)}^2}\doteq 4.7403\text{ cm } \\ {S}_1={\displaystyle \frac{h_1\cdot a}{2}}={\displaystyle \frac{4.7403\cdot 8.6}{2}}\doteq 20.3831{\text{cm}}^2 \\ V=S_1\cdot h=20.3831\cdot 24=489.1941{\text{cm}}^3 \end{gathered}$$

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