2008 AMC 10A Problems/Problem 20
Problem
Trapezoid has bases and and diagonals intersecting at Suppose that , , and the area of is What is the area of trapezoid ?
Solution
Solution 1
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 .
Solution 2
We denote with length and with length (which follows from similar triangles), and we denote . Note that . The areas of triangles and combined are . Thus, , as desired. -mop
See also
2008 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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