SOLUTION: Find the are of an equilateral triangle of side a.

Question 1008228: Find the are of an equilateral triangle of side a.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

RELATED QUESTIONS
Find the area of an equilateral triangle with side 12. (answered by ewatrrr)

Find the length of a side of an equilateral triangle with a height of... (answered by Theo,MathTherapy)

Find the area of an equilateral triangle, side a, in terms of a. (answered by lwsshak3)

Find the length of a side of an equilateral triangle whose altitude is 17.32... (answered by nerdybill)

Find the area of an equilateral triangle w/ a side of 6 inches (answered by Socom491)

Find the area of an equilateral triangle in which each side has a length of... (answered by drj)

Find the perimeter of an equilateral triangle with a side measure of... (answered by RAY100)

Find the side length of a equilateral triangle with an area of 12 radical... (answered by Gogonati,poliphob3.14,richard1234)

Find the area of an equilateral triangle given a side length of 8... (answered by unlockmath)