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

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- Oct 23rd 2009, 06:33 AMcaptaintoast87Pythagorean 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, 07:12 AMmathaddict
HI

Draw a triangle , call it $\displaystyle \triangle ABC $

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

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

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

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

$\displaystyle

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

$