1 / 32

11.1 Angle Measures in Polygons

11.1 Angle Measures in Polygons. Sum of measures of interior angles. # of triangles. # 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.

ayanna
Download Presentation

11.1 Angle Measures in Polygons

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 11.1 Angle Measures in Polygons

  2. Sum of measures of interior angles # of triangles # 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. Ex: 2 Find the value of x in the polygon x 126 100 143 130 117 126 + 130 + 117 + 143 + 100 + x = 720 616 + x = 720 x = 104

  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. Interior Angles Exterior Angles Two more important terms

  9. 2 1 3 5 4 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 625. 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 Triangle 30 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. 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. What is the area of this regular hexagon? 41.569 units2 4 The area of an equilateral triangle A = 6.9282 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. (It MUST be perpendicular to the side.)

  26. 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. Area of a Regular Polygon: A = ½ aP 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. Perimeter is 56 feet Apothem is 8.45 feet 7 ft What is the area? Area = .5 • 8.45 • 56 Area = 236.6 ft2

  31. Let's Practice 11.2 WorksheetPractice B ODDS

  32. Homework Worksheets’ EVENS

More Related