Understanding Areas of Regular Polygons
Learn the definitions and properties related to regular polygons, such as center, radius, central angle, apothem, and area calculations using special right triangles and trigonometric functions.
Understanding Areas of Regular Polygons
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Presentation Transcript
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
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.
Find the area of a regular pentagon with perimeter of 40 centimeters.
Find the area of a regular octagon with a perimeter of 72 inches.
Find the area of a regular polygon with 11 sides inscribed in a circle with a radius of 12.
