Difference between revisions of "2018 AMC 10B Problems/Problem 24"
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draw(A--B--C--D--E--F--cycle); | draw(A--B--C--D--E--F--cycle); | ||
| − | label("$A$",A, | + | label("$A$",A,NW); |
| − | label("$B$",B, | + | label("$B$",B,NE); |
label("$C$",C,ESE); | label("$C$",C,ESE); | ||
| − | label("$D$",D, | + | label("$D$",D,SE); |
| − | label("$E$",E, | + | label("$E$",E,SW); |
label("$F$",F,WSW); | label("$F$",F,WSW); | ||
Revision as of 16:31, 16 February 2018
Problem
Let 
be a regular hexagon with side length 
. Denote 
, 
, and 
the midpoints of sides 
, 
, and 
, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of 
and 
?
Answer: 
Solution
![[asy] pair A,B,C,D,E,F,W,X,Y,Z; A=(0,sqrt(3)); B=(1,sqrt(3)); C=(3/2,sqrt(3)/2); D=(1,0); E=(0,0); F=(-1/2,sqrt(3)/2); draw(A--B--C--D--E--F--cycle); label("$A$",A,NW); label("$B$",B,NE); label("$C$",C,ESE); label("$D$",D,SE); label("$E$",E,SW); label("$F$",F,WSW); [/asy]](http://latex.artofproblemsolving.com/b/8/c/b8c72cdeef18b84a494d53360b7ef4b444ade9d3.png)
See Also
| 2018 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 | ||
| 2018 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 19 |
Followed by Problem 21 |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
