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Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
For a regular hexagon, the length of the radius is 12 in. Find the length of the radius for the inscribed circle for this hexagon.
To find:
The length of the radius of inscribed circle in a hexagon.
1) Any radius of a regular polygon bisects the angle at the vertex to which it is drawn.
2) Any apothem of a regular polygon bisects the side of the polygon to which it is drawn.
3) The measure of any central angle of a regular polygon of n sides is given by
4) The radius inscribed circle in a hexagon is equal to the apothem of the hexagon.
Calculation:
Consider a regular hexagon ABCDEF with QE as radius and QG as apothem.
It is given that the length of the radius of the regular hexagon ABCDEF is 12 in. i.e., QD = 12 in.
Use the formula of central angle,
Substitute n = 6 in
Therefore,
With
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