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Understanding the Area and Apothem of Regular Polygons

This section explores key concepts related to the area of regular polygons, focusing on the apothem—defined as the distance from the center to the midpoint of any side, which bisects the central angle. The central angle of a regular polygon is calculated as 360 degrees divided by the number of sides. We will also apply these concepts through practical problems, including finding the area of regular hexagons, pentagons, and octagons using their respective apothems and perimeters.

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Understanding the Area and Apothem of Regular Polygons

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  1. Area of a Regular Polygon Section 11.6

  2. Apothem of a polygon – Distance from the center to the middle of any side of a polygon. The apothem bisects the central angle. • Central angle of a regular polygon – Angle formed by two lines from the center to consecutive vertices of a polygon. The measure of the central angle is 360/number of sides.

  3. Area of a regular polygon a = apothem P = perimeter of the polygon

  4. Find the area of the regular hexagon with the given information below 6 in 6 in

  5. Find the area of the regular pentagon with the given information below 5 in 4 in

  6. Find the area of the regular octagon with the given information below: 8 yd

  7. Find the area of the regular hexagon below 10 cm

  8. Practice Problems • p.765: 6-9, 14-16, 19-21,

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