Transcript Notes 76: 11.6 Areas of Regular Polygons

Notes 76:
11.6 Areas of Regular
Polygons
THEOREM 11.11: AREA OF A REGULAR
POLYGON
• The area of a regular n-gon with side length s
is half the product of the apothem, a, and
the perimeter, P, so
1
1
A = aP, or A = aP
2
2
Find angle measures in a regular
polygon
• In the diagram, ABCDEF is a regular hexagon inscribed in
G. Find each angle measure.
a. m  EGF
b. m  EGH
c. m  HEG
• Find the measure of a central angle of a regular polygon
with the given number of sides. Round answers to the
nearest tenth of a degree, if necessary.
• 15 sides
• 32 sides
• A regular octagon has a radius of 11.5
inches. What is the length of its apothem?
Round your answer to the nearest tenth.
Find the area of a regular polygon
• A wooden coaster is a regular octagon with 3
centimeter sides and a radius of about 3.92
centimeters. What is the area of the coaster?
Find the perimeter and area of a
regular polygon
• A regular nonagon is inscribed in a circle with
radius 5 units. Find the perimeter P and area A of
the nonagon.
• Find the area of the shaded region. Round answers to the
nearest tenth, if necessary
• Find the area of the shaded region. Round answers to the
nearest tenth, if necessary