2001 AMC 8 Problems/Problem 11
Problem
Points , , and have these coordinates: , , and . The area of quadrilateral is
Solution #1
This quadrilateral is a trapezoid, because but is not parallel to . The area of a trapezoid is the product of its height and its median, where the median is the average of the side lengths of the bases. The two bases are and , which have lengths and , respectively, so the length of the median is . is perpendicular to the bases, so it is the height, and has length . Therefore, the area of the trapezoid is
Solution 2
Using the diagram above, the figure can be divided along the x-axis into two familiar regions that do not overlap: a right triangle and a rectangle. Since the areas do not overlap, the area of the entire trapezoid is the sum of the area of the triangle and the area of the rectangle.
Video Solution
https://youtu.be/5gldUJaZZCg Soo, DRMS, NM
See Also
2001 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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