information:extraction
Using trigonometry

Using trigonometry, the area of a triangle with any two sides a {\displaystyle a} and b {\displaystyle b}, and an angle C {\displaystyle C} between them is

Each angle of an equilateral triangle is 60°, so

The sine of 60° is 3 2 {\displaystyle {\tfrac {\sqrt {3}}{2}}}. Thus

since all sides of an equilateral triangle are equal.