Difference between revisions of "2016 AMC 8 Problems/Problem 22"
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fill((3,0)--(2,4)--(1.5,3)--cycle, black); | fill((3,0)--(2,4)--(1.5,3)--cycle, black); | ||
− | label("A",(3.05,4.2)); | + | label("$A$",(3.05,4.2)); |
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− | label("D",(0,4.2)); | + | label("$D$",(0,4.2)); |
− | label("E", (0,-0.2)); | + | label("$E$", (0,-0.2)); |
− | label("F", (3,-0.2)); | + | label("$F$", (3,-0.2)); |
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Revision as of 12:39, 23 November 2016
Rectangle below is a rectangle with . What is the area of the "bat wings" (shaded area)?
Solution
The area of the trapezoid containing the shaded region and the two isosceles triangles is . Next we find the height of each triangle to calculate their area. The triangles are similar, and are in a ratio, so the height of the bigger one is 3, while the height of the smaller one is 1. Thus, their areas are and . Subtracting these areas from the trapezoid, we get . Therefore, the answer is .
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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 |
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