Question 611934
    The altitude of an equilateral triangle is 3root3, find its area?
.
First, find the length of the base:
Let b = length of base
then applying Pythagorean theorem:
{{{(b/2)^2 + (3sqrt(3))^2 = b^2}}}
{{{b^2/4 + (9*3) = b^2}}}
{{{b^2/4 + 27 = b^2}}}
{{{b^2 + 108 = 4b^2}}}
{{{108 = 3b^2}}}
{{{36 = b^2}}}
{{{6 = b}}}
.
area of triangle is
(1/2)bh
{{{(1/2)(6)(3sqrt(3))}}}
{{{(3)(3sqrt(3))}}}
{{{9sqrt(3))}}} square units