Problem:
An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is , what is the area of the hexagon?
Answer Choices:
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Solution:
The equilateral triangle can be divided into smaller congruent equilateral triangles, each with area of and side length , as shown. Then the original equilateral triangle has perimeter . A hexagon with perimeter can be divided into congruent equilateral triangles, each with area of . Therefore the area of the hexagon is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions