Question 1008228
you can look it up or you can derive it.


if you look it up, you will see that the area of an equilateral triangle = a^2 * sqrt(3) / 4.


you derive it by using pythagorus rule for right triangles and solve for h in terms of a.


you will get h = a * sqrt(3)/2


area of any triangle = 1/2 * b * h which then becomes area of equilateral triangle = 1/2 * a * a * sqrt(3) / 2 which then becomes area of equilateral triangle = a^2 * sqrt(3) / 4.


either way, you will get area of equilateral triangle = a^2 * sqrt(3) / 4.


for example, if you let a = 20, then the area should be equal to 20^2 * sqrt(3) / 4 which would be equal to 100 * sqrt(3)


the height, by pythagorus, would be equal to sqrt(20^2 - 10^2) = sqrt(400-100) = sqrt(300) = sqrt(100*3) = 10*sqrt(3).


you have a height of 10 * sqrt(3) and a base of 20 and a hypotenuse of 20.


area = 1/2 * base * height = 1/2 * 20 * 10 * sqrt(3) which is equal to 100 * sqrt(3).


it checks out, so the formula for area in terma of a must be correct.


area of equilateral triangle = a^2 * sqrt(3) / 4.