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)
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4
Not sure how to begin, thanks very much
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}
$