A circle is inscribed in an equilateral triangle. The radius of the circle is 2 cm. What is the area of the triangle?
- A. 12\sqrt{3} square cm ✓
- B. 12 square cm
- C. 9\sqrt{3} square cm
- D. 9 square cm
Correct Answer: A. 12\sqrt{3} square cm
Explanation
For an equilateral triangle, the inradius r = \frac{a}{2\sqrt{3}}. With r=2, the side a = 4\sqrt{3} cm. The area is \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4}(48) = 12\sqrt{3} sq cm.
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