Question

HS LEVEL GEO QUESTION!!! special right triangles

Calculate the area of the equilateral triangle below, which has an altitude of 15 inches. Please explain how to solve question

Answer 1

`\textit{height of an equilateral triangle}\\\\ h=\cfrac{s√(3)}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=15 \end{cases}\implies 15=\cfrac{s√(3)}{2}\implies 30=s√(3) \\\\\\ \cfrac{30}{√(3)}=s\implies \cfrac{30}{√(3)}\cdot \cfrac{√(3)}{√(3)}=s\implies \cfrac{30√(3)}{3}=s\implies 10√(3)=s \\\\[-0.35em] ~\dotfill`

`\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2√(3)}{4} ~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=10√(3) \end{cases}\implies A=\cfrac{(10√(3))^2 √(3)}{4}\implies A=\cfrac{(10^2 (√(3))^2) √(3)}{4} \\\\\\ A=\cfrac{(100)(3)√(3)}{4}\implies A=\cfrac{300√(3)}{4}\implies A=75√(3)`