7 Circles and Hexagon

Geometry Level 3

Seven unit circles were arranged inside regular hexagon as shown. What is the side length of the Hexagon?

Round your answer to three decimal places.


The answer is 3.155.

Ahmed Almubarak by Ahmed Almubarak , 38, Iraq

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1 solution

Ahmed Almubarak
May 5, 2018

From the picture:

S i d e L e n g t h = 2 + 2 X Side\quad Length\quad =\quad 2\quad +\quad 2X

X = 1 tan ⁡ 60 = 0.57735 X\quad =\quad \frac { 1 }{ \tan { 60 } } =\quad 0.57735

S i d e L e n g t h = 2 + 2 ∗ 0.57735 Side\quad Length\quad =\quad 2\quad +\quad 2\quad *\quad 0.57735 = 3.1547 =\boxed { 3.1547 }

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