Difference between revisions of "2018 AMC 10B Problems/Problem 24"

(Problem)
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==Problem==
 
==Problem==
  
Given regular hexagon ABCDEF with side length 1, define X to be the midpoint of side AB, Y to be the midpoint of side CD, and Z to be the midpoint of side EF, as shown. What is the area of the hexagon formed by the intersection of triangles ACE and XYZ
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Let ABCDEFG be a regular hexagon with side length 1. Denote X, Y, and Z the midpoints of sides (segment) AB, (segment) CD, and (segment) EF, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of (insert) triangle symbol) ACE and (insert triangle symbol) XYZ?
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choices?
 
  
 
Answer: 15sqrt(3)/32
 
Answer: 15sqrt(3)/32

Revision as of 16:03, 16 February 2018

(This is not the exact wording of the question)

Problem

Let ABCDEFG be a regular hexagon with side length 1. Denote X, Y, and Z the midpoints of sides (segment) AB, (segment) CD, and (segment) EF, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of (insert) triangle symbol) ACE and (insert triangle symbol) XYZ?


Answer: 15sqrt(3)/32