2017 AMC 8 Problems/Problem 18
Problem 18
In the non-convex quadrilateral shown below,
is a right angle,
,
,
, and
.
What is the area of quadrilateral
?
Solution
We first connect point with point
. We can see that it is a 3-4-5 right triangle. We can see that
is a right triangle [I NEED SOMEBODY TO PROVE THIS] , therefore
is
, by the 5-12-13 Pathagorean 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
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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