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In an equilateral triangle, the altitude drawn from a vertex to the opposite side is called .
The base $BC$ of an equilateral triangle $\triangle ABC$ is divided equally by the altitude, hence $BD = CD = $.
Solving for the altitude $AD$: $AD = \frac{\sqrt{3}a}{}$.
Using Pythagorean theorem, in $\triangle ABD$, $BD^2 + AD^2 = $.
The area of triangle $\triangle ABC$ can also be calculated as $\frac{1}{2} \times BC \times AD = \frac{\sqrt{3}}{} a^2$.
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