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Honors Geometry Section 5.5 Areas of Regular Polygons

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Recall that a regular polygon is a polygon that is both equilateral and equiangular.

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The center of a regular polygon is the point which is equidistant from the two vertices. A radius of a regular polygon is a segment from the center to one of the vertices.

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An apothem of a regular polygon is a segment from the center perpendicular to a side. An apothem also _______the side of a regular polygon. bisects

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The area of any regular n-gon can be found by dividing the regular polygon into n congruent triangles. This is done by drawing the radii of the regular polygon. A reg polygon = area of 1 triangle times the number of triangles.

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So the formula for the area of a regular polygon is

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Examples: Find the (exact) area of each regular polygon.

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