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imc

geometry intermediate

Problem

An equilateral triangle has side length . What is the area of the region containing all points that are outside the triangle but not more than units from a point of the triangle?
(A)
(B)
(C)
(D)
Solution
After a quick sketch of the problem, one can deduce that there are rectangles in the figure, each with side length and width . Therefore, the combined areas of the rectangles is . The other three regions are circle-shaped areas, probably expressed in some form of . Answer choices , , are impossible because they either lack an integer or in the answer, and is impossible since clearly does not belong to the rectangle or the circular areas. We can conclude that the only choice left is .
Final answer
B