Difference between revisions of "2002 AMC 8 Problems/Problem 15"
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− | + | == Problem == | |
− | == Problem | ||
Which of the following polygons has the largest area? | Which of the following polygons has the largest area? | ||
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<asy> | <asy> | ||
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<math> \textbf{(A)}\text{A}\qquad\textbf{(B)}\ \text{B}\qquad\textbf{(C)}\ \text{C}\qquad\textbf{(D)}\ \text{D}\qquad\textbf{(E)}\ \text{E} </math> | <math> \textbf{(A)}\text{A}\qquad\textbf{(B)}\ \text{B}\qquad\textbf{(C)}\ \text{C}\qquad\textbf{(D)}\ \text{D}\qquad\textbf{(E)}\ \text{E} </math> | ||
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+ | ==Solution== | ||
+ | Each polygon can be partitioned into unit squares and right triangles with sidelength <math>1</math>. Count the number of boxes enclosed by each polygon, with the unit square being <math>1</math>, and the triangle being being <math>.5</math>. A has 5, B has 5, C has 5, D has 4.5, and E has 5.5. Therefore, the polygon with the largest area is <math>\boxed{\textbf{(E)}\ \text{E}}</math>. | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2002|num-b=14|num-a=16}} |
Revision as of 18:47, 23 December 2012
Problem
Which of the following polygons has the largest area?
Which of the following polygons has the largest area?
Solution
Each polygon can be partitioned into unit squares and right triangles with sidelength . Count the number of boxes enclosed by each polygon, with the unit square being , and the triangle being being . A has 5, B has 5, C has 5, D has 4.5, and E has 5.5. Therefore, the polygon with the largest area is .
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 AJHSME/AMC 8 Problems and Solutions |