1. 11.1
Angle Measures
in Polygons

2. Sum of measures of interior angles
# of triangles
Sum of measures of interior angles
# of sides
1(180)=180 3 1
2(180)=360 4 2 3
3(180)=540 5 6 4
4(180)=720
n-2
(n-2) • 180 n

3. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

4. If a regular convex polygon has n sides, then the measure of one of the interior angles is

5. Ex. 1 Use a regular 15-gon to answer the questions.
Find the sum of the measures of the interior angles.
Find the measure of ONE interior angle
2340°
156°

6. x = 104 Ex: 2 Find the value of x in the polygon x 126 100 143 130 117

7. Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have?
One interior angle
A regular dodecagon

8. Two more important terms
Interior Angles
Exterior Angles

9. 1 2 3 4 5
The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°.

10. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°.1 3 2

11. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°.1 2 4 3

12. The measure of each exterior angle of a regular polygon is

13. Ex. 4 Find the measure of ONE exterior angle of a regular 20-gon.
18°

14. Ex. 5 Find the measure of ONE exterior angle of a regular heptagon.
51.4°

15. Ex. 6 The sum of the measures of five interior angles of a hexagon is What is the measure of the sixth angle?
95°

16. Let’s practice!
11.1 Worksheet

17. 11.2
Area of
Regular Polygons

18. Area of an Equilateral Triangle30 30 s s 60 60 s

19. Ex: 1 Find the area of an equilateral triangle with 4 ft sides.

20. A Circle can be circumscribed around any regular polygon

21. VERTICES

22. A Central Angle is an angle whose vertex is the center and whose sides are two consecutive radii
A RADIUS joins the center of the regular polygon with any of the vertices

23. How many equilateral triangles make up a regular Hexagon?
Equal Sides s
Equal Angles
How many equilateral triangles make up a regular Hexagon?
What is the area of each triangle?
What is the area of the hexagon?
6 • (the area of the triangle)

24. 41.569 units2 What is the area of this regular hexagon? 4
The area of an equilateral triangle
A =
The area of our equilateral triangle in this example
How many identical equilateral triangles do we have? 6
A = 6 * (6.9282)
The area of our hexagon in this example

25. An APOTHEM is the distance between the center and a side
An APOTHEM is the distance between the center and a side. (It MUST be perpendicular to the side.)

26. You need to know the apothem and perimeter
How to find the
Area of ANY REGULAR POLYGON
You need to know the apothem and perimeter
Area = (1/2)•a•P
or A = .5•a•P

27. A = ½ aP a Area of a Regular Polygon:
A = .5 (apothem) (# of sides)(length of each side) a

28. A Regular Octagon
7 ft

29. 360/8=45
22.5° 45 x 7
3.5 ft

30. Area = 236.6 ft2 Area = .5 • 8.45 • 56 Perimeter is 56 feet
Apothem is 8.45 feet
7 ft
What is the area?
Area = .5 • 8.45 • 56
Area = ft2

31. 11.2 Worksheet Practice B ODDS
Let's Practice
11.2 Worksheet Practice B ODDS

32. Homework
Worksheets’ EVENS