Difference between revisions of "2017 AMC 8 Problems/Problem 18"
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In the non-convex quadrilateral <math>ABCD</math> shown below, <math>\angle BCD</math> is a right angle, <math>AB=12</math>, <math>BC=4</math>, <math>CD=3</math>, and <math>AD=13</math>. What is the area of quadrilateral <math>ABCD</math>? | In the non-convex quadrilateral <math>ABCD</math> shown below, <math>\angle BCD</math> is a right angle, <math>AB=12</math>, <math>BC=4</math>, <math>CD=3</math>, and <math>AD=13</math>. What is the area of quadrilateral <math>ABCD</math>? | ||
Revision as of 14:08, 18 January 2021
Contents
Problem
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 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
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 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.