Problem:
An equiangular octagon has four sides of length and four sides of length , arranged so that no two consecutive sides have the same length. What is the area of the octagon?
Answer Choices:
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Solution:
The octagon can be partitioned into five squares and four half squares, each with side length , so its area is
The octagon can be obtained by removing four isosceles right triangles with legs of length from a square with sides of length . Thus its area is
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Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions