Calculate the area of an equilateral triangle whose side is 6 cm.

To calculate the area of ​​this equilateral triangle, we will use the fact that the area S of any triangle can be found knowing the length of the two sides and the angle between them using the following formula:

S = b * c * sin (α) / 2,

where b and c are two sides of this triangle, and α is the angle between these sides.

According to the condition of the problem, this triangle is equilateral and the length of its sides is 6 cm.

All angles of this triangle are also equal to each other and are 60 °.

Therefore, the area S of this triangle is:

S = 6 * 6 * sin (60 °) / 2 = 36 * (√3 / 2) / 2 = 9√3 cm².

Answer: the area of ​​this triangle is 9√3 cm².