2000 AMC 10 Problem 18

Problem 18 of 25IntermediateGeometry Arithmetic

Charlyn walks completely around the boundary of a square whose sides are each

5

km long. From any point on her path she can see exactly

1

km horizontally in all directions. What is the area of the region consisting of all points Charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?

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Solution

Inside the square, Charlyn sees everything except a central square of side

5 - 2 = 3,

an area of

25 - 9 = 16

square kilometers. Outside the square, the region is four rectangles each

5 \times 1

plus four quarter circles of radius

1,

an area of

4 \cdot 5 + \pi = 20 + \pi

square kilometers. The total area is

36 + \pi \approx 39

square kilometers. Thus, the correct answer is C.

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