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Four regular hexagons are drawn so as to form the design as shown in the given figure. If the perimeter of the design is 28cm, then the length of each side of the hexagon is ____ cm.

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Detailed Solution

Four regular hexagons are drawn so as to form the design as shown in the given figure. If the perimeter of the design is 28cm, then the length of each side of the hexagon is 2 cm.
Question Image

Question Image

Given that four regular hexagons and perimeter of the design = 28 cm.
We know that,
Perimeter of the hexagon = 14

\times

Length of one side of the hexagon
From figure,
Perimeter of the given design = Sum of all outer sides of the four hexagons
Here, this figure has 14 outer equal sides.
The perimeter of the design = 14

\times

Length of one side of the hexagon

\Rightarrow

28 = 14

\times

Length of one side of the hexagon

\Rightarrow \frac{28}{14}

= Length of one side of the hexagon
∴ Length of one side of the hexagon = 2 cm.
Hence, the length of each side of the hexagon is 2 cm.

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Four regular hexagons are drawn so as to form the design as shown in the given figure. If the perimeter of the design is 28cm, then the length of each side of the hexagon is ____ cm.