2012 AMC 10B Problems/Problem 19
Contents
Problem
In rectangle ,
,
, and
is the midpoint of
. Segment
is extended 2 units beyond
to point
, and
is the intersection of
and
. What is the area of quadrilateral
?
Solution
Note that the area of equals the area of
.
Since
. Now,
, so
and
so
Therefore,
hence our answer is
Solution 2
Notice that is a trapezoid with height
, so we need to find
.
, so
. Since
,
. The area of
is
See Also
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 AMC 10 Problems and Solutions |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.