# Math Help - Pythagorean Theorem?

1. ## Pythagorean Theorem?

How can I use algebra to show that the area of an equilateral triangle of side length S, is given by:

Area of the triangle(s)=(S^2)(Sqr root 3)
______________
4

Not sure how to begin, thanks very much

2. Originally Posted by captaintoast87
How can I use algebra to show that the area of an equilateral triangle of side length S, is given by:

Area of the triangle(s)=(S^2)(Sqr root 3)
______________
4

Not sure how to begin, thanks very much
HI

Draw a triangle , call it $\triangle ABC$

O is the midpoint of BC . AO is the height of the altitude of the triangle .

$AO=\sqrt{s^2-(\frac{s}{2})^2}$

$=\frac{s\sqrt{3}}{2}$

Area $=\frac{s\sqrt{3}}{2}\cdot s$

$
=\frac{s^2\sqrt{3}}{2}
$