Difference between revisions of "2018 AMC 10B Problems/Problem 24"
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<asy> | <asy> | ||
+ | pair A,B,C,D,E,F,W,X,Y,Z; | ||
+ | A=(0,0); | ||
+ | B=(1,0); | ||
+ | C=(3/2,sqrt(3)/2); | ||
+ | D=(1,sqrt(3)); | ||
+ | E=(0,sqrt(3)); | ||
+ | F=(-1/2,sqrt(3)/2); | ||
+ | W=(4/3,2sqrt(3)/3); | ||
+ | X=(4/3,sqrt(3)/3); | ||
+ | Y=(-1/3,sqrt(3)/3); | ||
+ | Z=(-1/3,2sqrt(3)/3); | ||
+ | draw(A--B--C--D--E--F--cycle); | ||
+ | draw(W--Z); | ||
+ | draw(X--Y); | ||
+ | draw(F--C--B--E--D--A); | ||
+ | label("$A$",A,SW); | ||
+ | label("$B$",B,SE); | ||
+ | label("$C$",C,ESE); | ||
+ | label("$D$",D,NE); | ||
+ | label("$E$",E,NW); | ||
+ | label("$F$",F,WSW); | ||
+ | label("$W$",W,ENE); | ||
+ | label("$X$",X,ESE); | ||
+ | label("$Y$",Y,WSW); | ||
+ | label("$Z$",Z,WNW); | ||
</asy> | </asy> | ||
Revision as of 17:29, 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
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.