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.
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