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Ann played a game as follows. From the starting position, she went straight 18 meters, then turned 36 degrees to the right. After that, she went straight again 18 meters, then turned 36 degrees to the right, ⋯⋯ and so on, until getting back to the starting position. What is the total distance that she walked in meters?

Question

Ann played a game as follows. From the starting position, she went straight 18 meters, then turned 36 degrees to the right. After that, she went straight again 18 meters, then turned 36 degrees to the right, ⋯⋯ and so on, until getting back to the starting position. What is the total distance that she walked in meters?

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Solution

The problem describes a regular polygon with sides of 18 meters. The sum of the interior angles of a polygon is (n-2)*180 degrees, where n is the number of sides.

Given that each turn is 36 degrees, the exterior angle of the polygon is 180 - 36 = 144 degrees.

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides of the polygon is 360/144 = 2.5.

However, a polygon cannot have a fractional number of sides. Therefore, the problem as stated does not make sense.

If we assume that each turn is actually 144 degrees (making the interior angle 36 degrees), then the number of sides of the polygon is 360/36 = 10.

In this case, the total distance walked is 10 * 18 = 180 meters.

This problem has been solved

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