2017 AMC 8 Problems/Problem 18
Problem 18
In the non-convex quadrilateral shown below,
is a right angle,
,
,
, and
. [asy]draw((0,0)--(2.4,3.6)--(0,5)--(12,0)--(0,0)); label("
", (0, 0), SW); label("
", (12, 0), ESE); label("
", (2.4, 3.6), SE); label("
", (0, 5), N);[/asy] What is the area of quadrilateral
?
Solution
We can see a Pythagorean triple's two longer lengths: 12, 13. So BD should be 5. This is certainly the case because , which is
. Thus the area of triangle ABD is
. So
, or
.
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.