Skip to main content

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?2?

Answer choices

Show solution

Solution

Since the base 22 equals two radii, the radius is 1.1. The trefoil is made of four equilateral triangles and four circular segments, which reassemble into four 60∘60^\circ sectors of a circle of radius 1.1. Their total area is 4⋅60360π(1)2=23π.4 \cdot \dfrac{60}{360}\pi (1)^2 = \dfrac{2}{3}\pi. Thus, the correct answer is B.
AoPS wiki

Tagged: sector · area decomposition · equilateral triangle

More practice