ABCDEF is a regular hexagon- PR -1-3 AF - QS -1-3 BC- PQ parallel to RS- Also TE -1-3 FE - UD -1-3 CD and TU parallel to ED- Find the ratio of shaded regions to the hexagon ABCDEF-A- 1-4B- 8- 27C- 17- 54D- 1- 3E- none of these

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ABCDEF is a r...

Question

ABCDEF is a regular hexagon. PR= $\frac{1}{3}$ AF, QS= $\frac{1}{3}$ BC& PQ parallel to RS. Also TE= $\frac{1}{3}$ FE & UD= $\frac{1}{3}$ CD and TU parallel to ED. Find the ratio of shaded regions to the hexagon ABCDEF.

1:4

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8:27

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17:54

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1:3

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none of these

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Solution

The correct option is B 8:27
Solution:

A regular hexagon can be divided into 54 equal triangles as follows

Of which the shaded part constitutes $\frac{16}{54}$ part.

Hence, the answer is option (b)

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ABCDEF is a regular hexagon. PR= 13 AF, QS= 13 BC& PQ parallel to RS. Also TE= 13 FE & UD= 13 CD and TU parallel to ED. Find the ratio of shaded regions to the hexagon ABCDEF.

The correct option is B 8:27Solution: A regular hexagon can be divided into 54 equal triangles as follows Of which the shaded part constitutes 1654 part. Hence, the answer is option (b)

ABCDEF is a regular hexagon. PR= $\frac{1}{3}$ AF, QS= $\frac{1}{3}$ BC& PQ parallel to RS. Also TE= $\frac{1}{3}$ FE & UD= $\frac{1}{3}$ CD and TU parallel to ED. Find the ratio of shaded regions to the hexagon ABCDEF.

The correct option is B 8:27
Solution:

A regular hexagon can be divided into 54 equal triangles as follows

Of which the shaded part constitutes $\frac{16}{54}$ part.

Hence, the answer is option (b)