What is the area of an equilateral triangle with a side measuring 12 inches?
In getting for the area of an equilateral triangle, following the formula for a triangle given the two sides with an included angle:
A= 1/2 (absin(tetha))
Since, it is an equilateral triangle, it also has same angles
180/3 = 60 degrees, each angle is equivalent to 60 degrees
Since the sides are all equal, thus a=b
Substitute in the formula;
A=1/2 (a^2)(sin 60)
A= 1/2 (a^2) (sqrt 3 / 2)
Thus; the formula is now:
A= sqrt 3/4 (a^2)
where a is the side
A= sqrt3 / 4 (12)^2
A= 62.35 square inches