The figure ABCDEF is a regular hexagon. Evaluate the quotient Area of hexagon ABCDEFArea of △BCE.
Answer:
3
- Let O be the center of the regular hexagon ABCDEF.
Therefore, the area of hexagon ABCDEF=6× the area of △EOC - 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 - Area of hexagon ABCDEFArea of △BCE=6×Area of △EOC2×Area of △EOC=3