Problem:
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
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Solution:
The trefoil is constructed of four equilateral triangles and four circular segments, as shown. These can be combined to form four circular sectors. Since the radius of the circle is , the area of the trefoil is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions