¶ 2009 AMC8 Problem 9
Problem:
Construct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular pentagon, as shown. On a non-adjacent side of the pentagon, construct a regular hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?
Answer Choices:
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Solution:
One side of the triangle and one side of the octagon will each touch one other polygon. Two sides of the other polygons will touch other polygons. Make a table and add the appropriate number of sides.
The resulting polygon has sides.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions