Difference between revisions of "2018 AMC 10B Problems/Problem 24"
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| Line 15: | Line 15: | ||
size(9cm); | size(9cm); | ||
pen dps = fontsize(10); defaultpen(dps); | pen dps = fontsize(10); defaultpen(dps); | ||
| − | pair A = (1/2, | + | pair A = (1/2,\sqrt{3}); |
| − | pair B = (3/2, | + | pair B = (3/2, \sqrt{3}); |
| − | pair C = (2, | + | pair C = (2, \sqrt{3}/2); |
pair D = (3/2, 0); | pair D = (3/2, 0); | ||
pair E = (1/2, 0); | pair E = (1/2, 0); | ||
| − | pair F = (0, | + | pair F = (0,\sqrt{3}/2); |
</asy> | </asy> | ||
Revision as of 16:24, 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
import graph;
size(9cm);
pen dps = fontsize(10); defaultpen(dps);
pair A = (1/2,\sqrt{3});
pair B = (3/2, \sqrt{3});
pair C = (2, \sqrt{3}/2);
pair D = (3/2, 0);
pair E = (1/2, 0);
pair F = (0,\sqrt{3}/2);
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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. 
