Problem:
An equilateral triangle has side length . What is the area of the region containing all points that are outside the triangle and not more than units from a point of the triangle?
Answer Choices:
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Solution:
The region consists of three rectangles with length and width together with three sectors of circles with radius .
The combined area of the three sectors is the same as the area of a circle with radius , so the area of the region is
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The problems on this page are the property of the MAA's American Mathematics Competitions