SOLUTION: The altitude of an equilateral triangle is 3root3, find its area?

Algebra ->  Triangles -> SOLUTION: The altitude of an equilateral triangle is 3root3, find its area?      Log On


   

Question 611934: The altitude of an equilateral triangle is 3root3, find its area?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
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:
%28b%2F2%29%5E2+%2B+%283sqrt%283%29%29%5E2+=+b%5E2
b%5E2%2F4+%2B+%289%2A3%29+=+b%5E2
b%5E2%2F4+%2B+27+=+b%5E2
b%5E2+%2B+108+=+4b%5E2
108+=+3b%5E2
36+=+b%5E2
6+=+b
.
area of triangle is
(1/2)bh
%281%2F2%29%286%29%283sqrt%283%29%29
%283%29%283sqrt%283%29%29
9sqrt%283%29%29 square units