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Kaylis [27]
3 years ago
14

Find the area of an equilateral triangle with apothem 7 cm.

Mathematics
1 answer:
lbvjy [14]3 years ago
8 0
So hmm check the picture below

using the 30-60-90 rule, we get that much.. .bear in mind, an equilateral triangle has all equal sides, and therefore, all equal angles, so each angle is 60°, run a median through it from the center, and you split it in half

\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}\qquad 
\begin{cases}
s=\textit{length of one side}\\
----------\\
s=14\sqrt{3}
\end{cases}\implies A=\cfrac{(14\sqrt{3})^2\sqrt{3}}{4}
\\\\\\
A=\cfrac{14^2\cdot 3\sqrt{3}}{4}\implies A=\cfrac{588\sqrt{3}}{4}\implies A=147\sqrt{3}

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