Difference between revisions of "2008 AMC 8 Problems/Problem 4"
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Revision as of 00:30, 5 July 2013
Problem
In the figure, the outer equilateral triangle has area 
, the inner equilateral triangle has area 
, and the three trapezoids are congruent. What is the area of one of the trapezoids?
![[asy] size((70)); draw((0,0)--(7.5,13)--(15,0)--(0,0)); draw((1.88,3.25)--(9.45,3.25)); draw((11.2,0)--(7.5,6.5)); draw((9.4,9.7)--(5.6,3.25)); [/asy]](http://latex.artofproblemsolving.com/e/3/4/e34c3dede3f2bef33570072537b95ad87b3894f5.png)
Solution
The area outside the small triangle but inside the large triangle is 
. This is equally distributed between the three trapezoids. Each trapezoid has an area of 
.
See Also
| 2008 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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. 
