Difference between revisions of "2014 AMC 10A Problems/Problem 12"
(→Problem) |
|||
| Line 19: | Line 19: | ||
<math>\textbf{(E)}\ 108\sqrt{3}-9\pi </math> | <math>\textbf{(E)}\ 108\sqrt{3}-9\pi </math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AMC10 box|year=2014|ab=A|num-b=11|num-a=13}} | ||
| + | {{MAA Notice}} | ||
Revision as of 22:17, 6 February 2014
Problem
A regular hexagon has side length 6. Congruent arcs with radius 3 are drawn with the center at each of the vertices, creating circular sectors as shown. The region inside the hexagon but outside the sectors is shaded as shown What is the area of the shaded region?
![[asy] size(125); defaultpen(linewidth(0.8)); path hexagon=(2*dir(0))--(2*dir(60))--(2*dir(120))--(2*dir(180))--(2*dir(240))--(2*dir(300))--cycle; fill(hexagon,lightgrey); for(int i=0;i<=5;i=i+1) { path arc=2*dir(60*i)--arc(2*dir(60*i),1,120+60*i,240+60*i)--cycle; unfill(arc); draw(arc); } draw(hexagon,linewidth(1.8));[/asy]](http://latex.artofproblemsolving.com/8/6/a/86a43209ad5b7a8259bcc2551089f62d5295a3da.png)
Solution
See Also
| 2014 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
