Difference between revisions of "2008 AMC 10A Problems/Problem 20"
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Revision as of 10:54, 4 July 2013
Problem
Trapezoid has bases and and diagonals intersecting at . Suppose that , , and the area of is . What is the area of trapezoid ?
Solution
Since it follows that . Thus .
We now introduce the concept of area ratios: given two triangles that share the same height, the ratio of the areas is equal to the ratio of their bases. Since share a common altitude to , it follows that (we let denote the area of the triangle) , so . Similarly, we find and .
Therefore, the area of .
See also
2008 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.