Explain how the trigonometric area formula can be used to find the area of a equilateral triangle if you are only given the length of one side.

For sides a, b, and angle C between them, the area of a triangle is given by
.. AREA = (1/2)*a*b*sin(C)

For an equilateral triangle of side s, you have
.. a = b = s
.. C = 60°
Put these values into the formula.
.. AREA = (1/2)×s²×sin(60°)
.. AREA = s²×(√3)/4 . . . . . . . . . . . area of equilateral triangle given side length