2017 AMC 8 Problems/Problem 18
Problem
In the non-convex quadrilateral shown below, is a right angle, , , , and . What is the area of quadrilateral ?
Solution 1
We first connect point with point .
We can see that is a 3-4-5 right triangle. We can also see that is a right triangle, by the 5-12-13 Pythagorean triple. With these lengths, we can solve the problem. The area of is , and the area of the smaller 3-4-5 triangle is . Thus, the area of quadrialteral is
Solution 2
is a 3-4-5 right triangle. Then we can use Heron's formula to resolve the problem. The area of a triangle whose sides have lengths 5, 12, and 13 is \sqrt {s(s-5)(s-12)(s-13)}. S is the semi-perimeter of the triangle, s={\frac {5+12+13}{2}}= 15 . is
Video Solution
https://youtu.be/tJm9KqYG4fU?t=2812
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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