Hands-on math!

Equilateral triangle

An equilateral triangle is a triangle that has all 3 sides the same length:
All the angles of the triangle are the same too. They are all 60 degrees. This is because the angles of a triangle all add up to 180 degrees and if they are all equal then each one is 180/3 = 60 degrees!

Area of an equilateral triangle:
To compute the area of an equilateral triangle,
you must find its height:
To find this height, you must use the Pythagorean theorem:
The sides are a and the height (h) divides the base into halves (a/2) So, by the Pythagorean theorem:

    h = √ a 2 - (a/2) 2  = √ a 2 - a 2/4  = √ 3a 2/4 = a (√ 3 )/2
Now, the area of 1/2 of the equilateral triangle = (a/2) h/2 = (a h)/4
Two of them, which equals the area of the equilateral triangle =
    (a h)/2 = a (a√ 3 )/4 =
a2(√ 3  ) / 4