Question

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 hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?

$21$

$23$

$25$

$27$

$29$

Solution:

The triangle and octagon are at the ends of the chain, so each loses one side to a shared edge. The square, pentagon, hexagon, and heptagon are in the middle, so each loses two sides to shared edges.

The resulting polygon has $(3-1)+(4-2)+(5-2)+(6-2)+(7-2)+(8-1)=23$ sides.

Thus, B is the correct answer.

2009 AMC 8 Problem 9

Solution:

Problem 9 in Other Years