In the figure shown below, each of the points labeled $P$ through $X$ is a point of tangency between 2 circles. Each vertex of $\triangle{ABC}$ is the center of a circle. Each circle has a radius of $r$ cm. Which of the following expressions represents the area, in square centimeters, of $\triangle{ABC}$ ?

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Each side of the triangle has a length of $r+2r+r= 4r$.

Since the triangle is equilateral, it can be broken up into two $30-60-90$ triangles. The ratio of the base of this triangle to the height is $1:\sqrt{3}$.

Given a base of $2r$ (after the equilateral triangle is split in two), the corresponding height will be $2r\sqrt{3}$. Then we obtain the area of the entire triangle:

$$A=\frac{1}{2}bh$$ $$A = \frac{1}{2}(4r)(2r\sqrt{3})$$ $$A = \boxed{4r^2\sqrt{3}}$$