Problem:
A dart board is a regular octagon divided into regions as shown. Suppose that a dart thrown at the board is equally likely to land anywhere on the board. What is the probability that the dart lands within the center square?
Answer Choices:
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Solution:
Assume the octagon's edge is 1. Then the corner triangles have hypotenuse 1 and thus legs and area each; the four rectangles are 1 by and have area each, and the center square has area 1. The total area is . The probability that the dart hits the center square is .
The problems on this page are the property of the MAA's American Mathematics Competitions