Transcript Areas of Regular Polygons LESSON 10-3 Additional Examples A portion of a regular hexagon has an apothem and radii drawn.

Areas of Regular Polygons
LESSON 10-3
Additional Examples
A portion of a regular hexagon has an apothem
and radii drawn. Find the measure of each numbered angle.
m
1 = 360 = 60
m
2=2 m
m
2 = 1 (60) = 30
Substitute 60 for m
m
3 = 180 – (90 + 30) = 60
The sum of the measures of the angles
of a triangle is 180.
m
1 = 60, m
HELP
6
1
1
Divide 360 by the number of sides.
The apothem bisects the vertex angle of
the isosceles triangle formed by the radii.
2
2 = 30, and m
3 = 60.
1.
Quick Check
GEOMETRY
Areas of Regular Polygons
LESSON 10-3
Additional Examples
Find the area of a regular polygon with twenty 12-in. sides
and a 37.9-in. apothem.
p = ns
Find the perimeter.
p = (20)(12) = 240
Substitute 20 for n and 12 for s.
A=
1
ap
2
Area of a regular polygon
A=
1
(37.9)(240)
2
Substitute 37.9 for a and 240 for p.
A = 4548
Simplify.
The area of the polygon is 4548 in.2
HELP
Quick Check
GEOMETRY
Areas of Regular Polygons
LESSON 10-3
Additional Examples
A library is in the shape of a regular octagon. Each side is
18.0 ft. The radius of the octagon is 23.5 ft. Find the area of the library
to the nearest 10 ft2.
Consecutive radii form an isosceles triangle, as shown below,
so an apothem bisects the side of the octagon.
1
To apply the area formula A = 2 ap,
you need to find a and p.
HELP
GEOMETRY
Areas of Regular Polygons
LESSON 10-3
Additional Examples
(continued)
Step 1: Find the apothem a.
a2 + (9.0)2 = (23.5)2
a2 + 81 = 552.25
a2 = 471.25
a 21.7
Step 2: Find the perimeter p.
p = ns
p = (8)(18.0) = 144
HELP
Pythagorean Theorem
Solve for a.
Find the perimeter.
Substitute 8 for n and 18.0 for s,
and simplify.
GEOMETRY
Areas of Regular Polygons
LESSON 10-3
Additional Examples
(continued)
Step 3: Find the area A.
A = 1 ap
2
A
A
1 (21.7)(144)
2
1562.4
Area of a regular polygon
Substitute 21.7 for a and 144 for p.
Simplify.
To the nearest 10 ft2, the area is 1560 ft2.
Quick Check
HELP
GEOMETRY