2019 AIME I Problems/Problem 3
The 2019 AIME I takes place on March 13, 2019.
Problem 3
In , , , and . Points and lie on , points and lie on , and points and lie on , with . Find the area of hexagon .
Solution 1
We know the area of the hexagon to be . Since , we know that is a right triangle. Thus the area of is . Another way to compute the area is Then the area of . Preceding in a similar fashion for , the area of is . Since , the area of . Thus our desired answer is
Solution 2
Let be the origin. Noticing that the triangle is a 3-4-5 right triangle, we can see that , and . Using the shoelace theorem, the area is .
Video Solution
https://www.youtube.com/watch?v=4jOfXNiQ6WM
See Also
2019 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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All AIME Problems and Solutions |
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