2008 AMC 12A Problems/Problem 14
Problem
What is the area of the region defined by the inequality ?
$\mathrm{(A)}\ 3\qqurac {7}{2}\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ \frac{9}{2}\qquad\mathrm{(E)}\ 5$ (Error compiling LaTeX. Unknown error_msg)
Solution
Area is invariant under translation, so after translating left and up
units, we have the inequality
which forms a diamond centered at the origin and vertices at . Thus the diagonals are of length
and
. Using the formula
, the answer is
.
See also
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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 12 Problems and Solutions |
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