An equilateral triangle has an altitude of $5\sqrt{3}$ cm long. Find its area.

$\tan 60^\circ = \dfrac{5\sqrt{3}}{b/2}$

$b = 10 ~ \text{cm}$
 

 

$A = \frac{1}{2}(10)(5\sqrt{3})$

$A = 25\sqrt{3} ~ \text{cm}^2$