Triangular 80766

Calculate the volume of a regular triangular prism whose height is equal to the length of the base edge. Calculate the volume for the edge length a = 6 cm.

Correct answer:

V =  93.5307 cm³

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ h=a=6\text{cm} \\ {S}_1=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 6^2=9\sqrt{3}{\text{cm}}^2\doteq 15.5885{\text{cm}}^2 \\ V=S_1\cdot h=15.5885\cdot 6=54\sqrt{3}=93.5307{\text{cm}}^3 \end{gathered}$$

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