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There are two concentric convex hexagons. The smaller hexagon is formed by joining the midpoints of the lines joining the vertices of the bigger hexagon to its centre. Find the ratio of the area of the smaller hexagon to the area of the bigger hexagon.
  • a)
  • b)
    1 : 6
  • c)
    1 :4
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
There are two concentric convex hexagons. The smaller hexagon is forme...
The hexagons consist of 6-triangles as shown below, (figure not drawn to scale),

Considering any one triangle,

P and Q are the midpoints of AB and AC respectively.
By midpoint theorem, PQ is parallel to BC and its length is half of that of BC.

The same can be applied to the remaining triangles.
Thus, the area of the bigger hexagon will be four times the area of the smaller hexagon.
Hence, option 3.
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