2005 AMC 10A Problems/Problem 12
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 ?
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: