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


Answer:

3

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

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