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 17:22, 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 |
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