Objective

To find the area of a regular polygon.

Recall:

​Definition of a regular polygon

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

Area of a regular polygon

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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Parts of a regular polygon:

• 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.

Formula for area of a regular polygon:

Steps:

An example:

What if we don't know a side length?

​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

Your turn:

Let's kick it up a notch

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

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