The figure ABCDEFABCDEF is a regular hexagon. Evaluate the quotient Area of hexagon ABCDEFArea of BCEArea of hexagon ABCDEFArea of BCE.


Answer:

33

Step by Step Explanation:
  1. Let OO be the center of the regular hexagon ABCDEF.ABCDEF.
    A B C D E F O
    Therefore, the area of hexagon ABCDEF=6× the area of EOCABCDEF=6× the area of EOC
  2. In BCE,BCE,
    OO is the midpoint of BE.BE. Therefore OCOC is a median of the triangle BCEBCE.
    We know that the median of a triangle divides the triangle into two triangles with equal areas.
    Therefore, the area of EOC= area of BOCEOC= area of BOC
    or the area of BCE=2×BCE=2× the area of EOCEOC
  3. Area of hexagon ABCDEFArea of BCE=6×Area of EOC2×Area of EOC=3Area of hexagon ABCDEFArea of BCE=6×Area of EOC2×Area of EOC=3

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