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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

HS LEVEL GEO QUESTION!!! special right triangles Calculate the area of the equilateral-example-1

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\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)

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