Post on 15-Dec-2015
Areas of Regular Polygons 11.2
California State Standards 8: Solve problems involving perimeter and area.10: Find area of polygons16: Perform constructions19: Use trigonometric functions
theorem
Area of an Equilateral Triangle
ss
s
214 3A s
1 12 2 3A s s
12 2 3sA s
informal proof
s
s
60o
30o
2s
2 3s
214 3A s
example
4
214 3A s
214 3 (4)A
14 (16) 3A
4 3A
6.8 sq. unitsA
definition
Center of a PolygonThe center of its circumscribed circle.
Radius of a PolygonThe radius of its circumscribed circle.
definition
Apothem of a PolygonThe distance from the center to any side of the polygon.
radius
apothem
definition
Central Angle of a Regular PolygonAn angle whose vertex is the center andwhose sides contain two consecutive vertices.
definition
The Measure of a Central Angle of a Regular Polygon
72o360
n360
5
theorem
Area of a Regular Polygon P is the perimeter
a is the apothem
12A aP
s
a s
ss
s
1. 2pentA aP
125A aP#
125 5A a s#
125 5A as#
12A as#
informal proof
s
as
ss
s
sin 22.54
b
example
A regular octagon is inscribed in a circle with aradius 4 units. Find the area of the octagon.
4
22.5o
central angle = 45o
ba
s1.5b
3s
12A aP
3
12A aP
44.4 sq unitsA 1
2 3.7 24A
3.7a
cos 22.54
a
example
A regular octagon is inscribed in a circle with aradius 4 units. Find the area of the octagon.
4
22.5o
3
a3.7
example
The bottom of a glass is a regular dodecagon(12 sides) with a side length of 1.2 cm and aradius of 2.3 cm. What is the area of the bottom of the glass?
The bottom of a glass is a regular dodecagon(12 sides) with a side length of 1.2 cm and aradius of 2.3 cm. What is the area of the bottom of the glass?
example
1.20.6
2.3
215.8 cmA2 2 22.3 0.6a
14.4P 12(1.2)P
2.2 a
12 2.2 14.1A
12A aP
Today’s assignment p 672: 10 – 32 even
Find the area of the triangle.Find the measure of a central angle of a regular polygon with the given number of sides.
Find the area of the inscribed regular polygon shown.
Find the perimeter and area of the regular polygon.
Do the rest at home.