2017 AMC 8 Problems/Problem 18
Contents
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 is . Thus, the area of quadrilateral is
~CHECKMATE2021
Solution 2
is a 3-4-5 right triangle. So the area of is 6. Then we can use Heron's formula to compute the area of whose sides have lengths 5,12,and 13. The area of = , where s is the semi-perimeter of the triangle, that is Thus, the area of is 30, so the area of is ---LarryFlora
Video Solution (CREATIVE THINKING + ANALYSIS!!!)
~Education, the Study of Everything
Video Solution
https://www.youtube.com/watch?v=DU95-maui9U&ab_channel=WhyMath (http://youtube/DU95-maui9U)
~savannahsolver
Video Solution by OmegaLearn
https://youtu.be/51K3uCzntWs?t=2010
~ pi_is_3.14
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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 AJHSME/AMC 8 Problems and Solutions |
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