Question

Calculate the volume of the regular triangular pyramid with the base edges of length 9 inches and a height of length 8 inches.

Answer 1

so, the prism looks more or less like the picture below

now, notice the purple base, is a triangle with all sides of 9


`\bf \textit{area of an equalateral triangle}\\\\ A=\cfrac{s^2√(3)}{4}\qquad \begin{cases} s=\textit{length of one side}\\ ----------\\ s=9 \end{cases}\implies A=\cfrac{9^2√(3)}{4} \\\\ -----------------------------\\\\ \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{area of the base}\\ h=height\\ ----------\\ B=(81√(3))/(4)\\ h=8 \end{cases}\implies V=\cfrac{1}{3}\cdot \cfrac{81√(3)}{4}\cdot 8`