2005 AMC 10A Problems/Problem 12
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Problem
The figure shown is called a trefoil and is constructed by drawing circular sectors about the sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length ?
Solution
The area of the trefoil is equal to the area of a small equilateral triangle plus the area of four sectors with a radius of
minus the area of a small equilateral triangle.
This is equivalent to the area of four sectors with a radius of
.
So the answer is: