Difference between revisions of "2018 AMC 10B Problems/Problem 24"
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<asy> | <asy> | ||
| − | size( | + | import graph; |
| − | defaultpen( | + | size(9cm); |
| − | + | pen dps = fontsize(10); defaultpen(dps); | |
| − | + | pair A = (1/2,\sqrt3); | |
| − | + | pair B = (3/2, \sqrt3); | |
| + | pair C = (2, \sqrt3/2); | ||
| + | pair D = (3/2, 0); | ||
| + | pair E = (1/2, 0); | ||
| + | pair F = (0,\sqrt3/2); | ||
<\asy> | <\asy> | ||
Revision as of 16:22, 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>
import graph; size(9cm); pen dps = fontsize(10); defaultpen(dps); pair A = (1/2,\sqrt3); pair B = (3/2, \sqrt3); pair C = (2, \sqrt3/2); pair D = (3/2, 0); pair E = (1/2, 0); pair F = (0,\sqrt3/2); <\asy>
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. 
