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jmc

geometry intermediate

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 2?

problem
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 1, the area of the trefoil is
Final answer
\frac{2}{3}\pi