Question

If the altitude of an equilateral triangle is 12cm, find its area..

According to the answer sheet, answer is 83.1cm^2

Answer 1

yeah looks good to me

Answer 2

Erm.. How do you solve it?

Answer 3

you need the base. now since this is an equilateral triangle, all sides are equal. and that is what we are looking for, one of the sides. lets call is it x

Answer 4

ok..

Answer 5

then pythagoras tells you that
\[(\frac{1}{2}x)^2+12^2=x^2\]
\[12^2=x^2-\frac{1}{4}x^2\]
\[144=\frac{3}{4}x^2\]
\[x^2=144\times \frac{4}{3}=192\]
\[x=\sqrt{192}=6\sqrt{3}\]