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

1 Answer
Dec 9, 2014

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