1. Chapter 11 Areas of Polygons and Circles
Section 11.2
Area of Regular Polygons
Find the area of an equilateral triangle
Find the area of a regular polygon

2. Example 1 Area Equilateral Triangle Example 2 Area Regular Pentagon
Example 3 Area Regular Octagon
Example 4 Always, Sometimes, Or Never
CA Standard 12.0
Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. (Key)
Lesson 1 Contents

3. Find the area of an equilateral triangle
30°
60°
60°

4. Find the area of an equilateral triangle

5. Find the area of the triangle
Find the area of an equilateral triangle
Find the area of the triangle
The Triangle is equilateral with s = 11
Area Equilateral 
s = 11
Simplify
Answer: The triangle has area of square units
Example 1-1a

6. Find the area of the triangle
Find the area of an equilateral triangle
Find the area of the triangle
Answer: The triangle has area of square units
You 1

7. Center of circumscribed circle
Radius of circumscribed circle
Vertex is on the center, Sides connect consecutive vertices
Distance from center to any side of the polygons

8. To find the area of the hexagon, find the area of one triangle and multiply by 6
Height of the triangle is an apothem of the hexagon
Base of the triangle is a side of the hexagon
6 is the number of sides of the hexagon h b

9. Perimeter = ns = 5(5) = 25 units
Find the area of a regular polygon 5 4
Perimeter = ns = 5(5) = 25 units

10. Need to find the apothem and side length
Find the area of a regular polygon
Need to find the apothem and side length
Apothem = BD
Side Length = AC
Look at ABC
Example 1-3a

11. Find BD and AC BD = cos 36 AC = 2 sin 36
Find the area of a regular polygon
Find BD and AC
BD = cos 36
AC = 2 sin 36
Example 1-3b

12. Apothem = BD = cos 36 s = AC = 2(DC) = 2 sin 36
Find the area of a regular polygon
Apothem = BD = cos 36
s = AC = 2(DC) = 2 sin 36
Example 1-3c

13. Find the area of an octagon with radius 3 cm
Find the area of a regular polygon
Find the area of an octagon with radius 3 cm
Need to find the apothem and side length
This angle is half the Central Angle
45  2 = 22.5
Central Angle has measure 360  8 = 45
This length is half of s a s
Example 1-2a

14. Find the area of an octagon with radius 3 cm
Find the area of a regular polygon
Find the area of an octagon with radius 3 cm
Need to find a and s using the triangle a
22.5°
s = 6 sin 22.5
Example 1-2a

15. Find the area of an octagon with radius 3 cm
Find the area of a regular polygon
Find the area of an octagon with radius 3 cm
s = 6 sin 22.5 a s
Example 1-2a

16. Find the Area and Perimeter of the following pentagon
Find the measures of interior and exterior angles of polygons
Find the Area and Perimeter of the following pentagon
Answer: Area = 1125 tan 36  Square Units Perimeter = 150 tan 36  109 Units
You 2

17. Always
Always
Example 1-4a

18. HW # 48 Pg , 30-52