# Pythagorean Theorem?

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• Oct 23rd 2009, 07:33 AM
captaintoast87
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
• Oct 23rd 2009, 08:12 AM
mathaddict
Quote:

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}
$
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