Areas of Hexagons

Draw a hexagon. In each case below, find the ratio of the area of this hexagon to the new one formed by the crossing lines inside it.

  1. Connect each corner to the corner two locations clockwise.

  2. Connect the midpoint of each side to the midpoints of the adjacent sides.
  3. Connect the midpoint of each side to the midpoints of the non-adjacent sides (but not straight across.)

Source: Original.

Solution
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