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Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
Find the area of a regular hexagon whose apothem has length 9 in.
To find:
The area of a regular hexagon.
Formula:
If we are given the variables s and a, then we can solve for the area of the hexagon through the following formula:
In this equation, A is the area, P is the perimeter and a is the apothem.
We must calculate the perimeter using the side length and the equation
Where s is the side length.
Calculation:
The regular hexagon has apothem 9 in.
Let a = 9 in
The regular hexagon has six equal sides.
Sketch the following diagram:
To find side length (s):
Half of the length of one of the sides is part of a 30-60-90 triangle with the apothem. Thus:
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