1 / 23

Warm-Up

Warm-Up. Give the name of the polygon whose interior angle is sum is… 1. 3420 ° 2. 6300 ° 3. 21420 ° 4. 12780 ° 21-gon 37-gon 121-gon 73-gon 162.86 170.27 177.02 175.07 For each of the previous polygons give the measure of the each interior angle, assuming the polygon is regular. Warm-Up.

mina
Download Presentation

Warm-Up

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. Warm-Up • Give the name of the polygon whose interior angle is sum is… 1. 3420° 2. 6300° 3. 21420° 4. 12780° 21-gon 37-gon 121-gon 73-gon 162.86 170.27 177.02 175.07 • For each of the previous polygons give the measure of the each interior angle, assuming the polygon is regular.

  2. Warm-Up • Give the name of the regular polygon with each of its angles being… 1. 108° 2. 162° 3. 168° 4. 172.8° = 108 (n-2)180 = 108n 180n – 360 = 108n 180n = 108n + 360 72n = 360 n = 5 Pentagon = 168 (n-2)180 = 168n 180n – 360 = 168n 180n = 168n + 360 12n = 360 n = 30 30-gon = 162 (n-2)180 = 162n 180n – 360 = 162n 180n = 162n + 360 18n = 360 n = 20 20-gon = 172.8 (n-2)180 = 172.8n 180n – 360 = 172.8n 180n = 172.8n + 360 7.2n = 360 n = 50 50-gon

  3. Warm-Up • Give the measure of the exterior angles of a regular… 1. Quadrilateral 2. Hexagon 3. Nonagon 4. Dodecagon Remember all exterior angles add up to 360° = = 90° = = 60° = = 40° = = 30°

  4. Warm-Up • Give the name of the regular polygon whose exterior angles are… 1. 72° 2. 36° 3. 20° 4. 5° = = 5 Pentagon = = 10 Decagon = = 18 18-gon = = 72 72-gon

  5. Area of Regular Polygons

  6. Find the area • How can we find the area of this regular hexagon? 6

  7. Vocabulary • Radius – The distance from the center to one of the vertices of a regular polygon. • Apothem – The distance from the center to one of the sides of a polygon.

  8. Find the area • How can we find the area of this regular hexagon? 6

  9. Central Angles • What will be the measure of all of the central angles combined? • What is the measure of each of the central angles?

  10. Find the area • How can we find the area of this regular hexagon? 6

  11. Steps for Find the Area • Create congruent triangles from the center of the polygon. 6

  12. Steps for Find the Area 2. Find the central angle . 6 = = 60° 60°

  13. Steps for Find the Area 3. Find the apothem. Notice: that the apothem cuts the central angle and side length in half, and forms a right angle with the side length. 6 The apothem of the regular hexagon is 3 we can find this by using special right triangles, in some cases you may need to use trigonometry. (SOH CAH TOA) 30° 6 3√3 60° 60° 3

  14. Steps for Find the Area 4. Find the base of the triangle. In this case the base is given to us, in some problems we may need to use special right triangles or trigonometry to find the base. Base = 6 6 6 6 60° 6 6 6

  15. Steps for Find the Area 5. Find the area of the triangle. Base = 6 Apothem (or height) = 3√3 = 6 60°

  16. Find the Area • How can we use the same process to find the area of this regular pentagon? 6 The area of this regular pentagon is 61.95

  17. Steps for Find the Area 6. Multiply the area of the triangle by the number of triangles in the regular polygon. (6) = The area of this regular hexagon is . 6

  18. The area of a regular polygon • http://www.youtube.com/watch?v=4ogeQo_nV08

  19. Area of Regular Polygons • ∙s∙a∙n • a∙P • This means now to solve for the area of regular polygon we only need the apothem and a side length.

  20. Find the area of the regular polygon

  21. Find the area of the regular polygon

  22. Find the area of the regular polygon.

  23. Exit Ticket Homework • Find the area of the regular polygon. • Pg. 672: 9-24

More Related