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ISEE Lower Level
Mathematics Achievement

Total Length of Diagonals in a Regular Hexagon

Hard Geometry Shapes And Properties

Consider a regular hexagon, which is a six-sided polygon where all sides and angles are equal. Each interior angle of a regular hexagon can be calculated using the formula:

$$ ext{Interior Angle} = \frac{(n-2) \times 180^\circ}{n} $$

where $n$ is the number of sides. If the length of each side of the hexagon is $s$ units, what is the total length of the diagonals in this hexagon, knowing that a regular hexagon has 9 diagonals? Calculate the total length of all the diagonals, given that $s = 4$ units.

Hint

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