Question

What is the area of a equilateral triangle with a side of 12?

Answer 1

The formula for the Area of an equilateral triangle with side s is `A= (s^2sqrt(3))/4`

For an equilateral triangle, the sides are equal and the angles are equal. So each angle is 60 degrees. If we are to drop a vertical line from the vertex angle we divide the opposite side in two equal parts. The vertex angle is also equally divided into two. Thus, we form a 30°-60°-90° triangle.

The height , h, of the right triangle in terms of the sides (s) of the equilateral triangle is `(ssqrt(3))/2`

This height is also the height of the equilateral triangle whose base is s.

Generally the Area of any triangle is,

`A =( (base)*(height))/2`

plugging in the values,

`A = [(s)*(ssqrt(3))/2]/(2)`

`A = (s^2sqrt(3))/4`

`s = 12`

`A = (12^2sqrt(3))/(4)`

`A = 36sqrt(3)` square units