Question

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

Answer 1

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

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