2005 AMC 10A Problem 12

Problem 12 of 25IntermediateGeometry

The figure shown is called a trefoil and is constructed by drawing circular sectors about sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length

2?

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Solution

Since the base

2

equals two radii, the radius is

1.

The trefoil is made of four equilateral triangles and four circular segments, which reassemble into four

60^\circ

sectors of a circle of radius

1.

Their total area is

4 \cdot \dfrac{60}{360}\pi (1)^2 = \dfrac{2}{3}\pi.

Thus, the correct answer is B.

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