10.3 - Area of Regular Polygons

To find the area of a regular polygon.

​Definition of a regular polygon

A regular polygon has all sides equal and all interior angles equal.

The formula to determine area of a regular polygon is somewhat different than the area formulas we've learned previously.

Imagine inscribing the polygon inside a circle. Inscribing means each vertex touches the circle.

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So a segment from the center of the polygon to a vertex would be the radius of the circumscribed circle.​

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• The perpendicular distance from the center of the polygon to any side is called the apothem.

• The radius of a regular polygon is the ​distance from the center to a vertex.

​It's Right Triangle Time!

The formula calls for the apothem, which we have, and the perimeter, which we don't have. But if we draw in the radius, we can use trig to find half of one side, then multiply to find the perimeter.

​x

​So, you know the radius and that's it.