Question

What is the surface area of the pyrmid? The base is an equilateral triangle.

Answer 1

`\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2√(3)}{4} ~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=9 \end{cases}\implies A=\cfrac{9^2√(3)}{4} \\\\[-0.35em] ~\dotfill`

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{three standing triangles} }{3\left[\cfrac{1}{2}(\underset{b}{9})(\underset{h}{3}) \right]}~~ + ~~\stackrel{ \textit{base triangle} }{\cfrac{9^2√(3)}{4}}}\implies \cfrac{81}{2}+\cfrac{81√(3)}{4} ~~ \approx ~~ \text{\LARGE 75.57}~cm^2`