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What would be the area of a triangle formed by the medians of an equilateral triangle that has a side length of 12 cm?
The area of a triangle formed by the medians of an equilateral triangle would be (3/4) of the area of the original triangle.
The area of the original equilateral triangle can be calculated using the formula $$\frac{\sqrt{\ 3}}{4}a^2$$, where $$a$$ is the side length, giving the area of the original equilateral triangle to be $$\frac{\sqrt{\ 3}}{4}\times\ 12\times\ 12$$
This would give the area of the triangle formed by the medians to be $$\frac{\sqrt{\ 3}}{4}\times\ 12\times\ 12\times\ \frac{3}{4}=27\sqrt{\ 3}cm^2$$
Therefore, Option C is the correct answer.
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