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10-3 Areas of Regular Polygons

10-3 Areas of Regular Polygons. Definitions. Center of a regular polygon  the center of the circumscribed circle. Radius of a regular polygon  the distance from the center to a vertex. All radii of a figure are congruent.

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10-3 Areas of Regular Polygons

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  1. 10-3 Areas of Regular Polygons

  2. Definitions • Center of a regular polygon  the center of the circumscribed circle. • Radius of a regular polygon  the distance from the center to a vertex. All radii of a figure are congruent. • Central angle of a regular polygon  an angle formed by two radii drawn to consecutive vertices. All central angles are congruent. • Apothem of a regular polygon  the perpendicular distance from the center of the polygon to a side. Every apothem of a figure is congruent

  3. Theorem • The area of a regular polygon is equal to half the product of the apothem and the perimeter. • A= ½ aP • Apothems are going to be found using special right triangles, and sine, cosine, tangent functions.

  4. Find the area of a regular pentagon with perimeter of 40 centimeters.

  5. Find the area of a regular octagon with a perimeter of 72 inches.

  6. Find the area of a regular hexagon with apothem of 9.

  7. Find the area of a regular polygon with 11 sides inscribed in a circle with a radius of 12.

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