2008 AMC 12B Problems/Problem 13
Problem
Vertex of equilateral is in the interior of unit square . Let be the region consisting of all points inside and outside whose distance from is between and . What is the area of ?
Solution
The region is the shaded area:
We can find the area of the shaded region by subtracting the pentagon from the middle third of the square. The area of the middle third of the square is . The pentagon can be split into a rectangle and an equilateral triangle.
The base of the equilateral triangle is and the height is . Thus, the area is .
The base of the rectangle is and the height is the height of the equilateral triangle minus the height of the smaller equilateral triangle. This is: Therefore, the area of the shaded region is
See Also
2008 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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