Transcript 11-4 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.
• 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 hexagon with apothem of
9.
• Find the area of a regular polygon with 11
sides inscribed in a circle with a radius of 12.