2006 AMC 10B Problems/Problem 6
Problem
A region is bounded by semicircular arcs constructed on the side of a square whose sides measure , as shown. What is the perimeter of this region?
Solution
Since the side of the square is the diameter of the semicircle, the radius of the semicircle is .
Since the length of one of the semicircular arcs is half the circumference of the corresponding circle, the length of one arc is .
Since the desired perimeter is made up of four of these arcs, the perimeter is .
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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