2002 AMC 12P Problems/Problem 19
Contents
[hide]Problem
In quadrilateral , and Find the area of
Solution
Solution 1
Draw parallel to and draw and , where and are on .
It is clear that triangles and are congruent triangles. Therefore, and .
Therefore, and the area of trapezoid is .
It remains to find the area of triangle , which is .
Therefore, the total area of quadrilateral is .
Solution 2
Extend and to meet at . Then triangle is equilateral, as . Thus, .
Note and Then, the area of triangle is . As triangle is equilateral, its area is .
The area of is the area of triangle minus the area of triangle , or .
~Michw08
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
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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