A circle is inscribed in a regular triangle with a side equal to 12 cm. Find its area.

The area of a circle is found by the formula:
S = ∏ * r².
The radius of a circle inscribed in a regular (equilateral) triangle is:
r = a√3 / 6, where a is the side of the triangle. Find the radius of the circle:
r = 12√3 / 6 = 2√3 (cm).
Substituting the found value of the radius into the area formula, we find the area:
S = ∏ * r² = ∏ * (2√3) ² = 12∏ (cm²).
Answer: the area of the circle is 12∏ cm².

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