1 / 22

Part 1 - Areas of Polygons

Part 1 - Areas of Polygons. Using Trigonometry. Review. Find the missing side. A. B. C. D. Ex. 1 Find the Area of a Rectangle. Using your knowledge of area of a triangle, right triangle trigonometry and the Pythagorean Theorem. Find the area of the rectangle below.

mnesbitt
Download Presentation

Part 1 - Areas of 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. Part 1 - Areas of Polygons Using Trigonometry

  2. Review Find the missing side. A. B. C. D.

  3. Ex. 1 Find the Area of a Rectangle • Using your knowledge of area of a triangle, right triangle trigonometry and the Pythagorean Theorem. Find the area of the rectangle below.

  4. Ex. 2 Find the Area of a Square • Using your knowledge of area of a triangle, right triangle trigonometry and the Pythagorean Theorem. Find the area of the square below.

  5. Ex. 3 Find the Area of a Triangle • Using your knowledge of area of a triangle, right triangle trigonometry and the Pythagorean Theorem. Find the area of the triangle below.

  6. Ex. 4 Find the Area of a Rhombus • Using your knowledge of area of a triangle, right triangle trigonometry and the Pythagorean Theorem. Find the area of the Rhombus below. 5 4 5 5 4 5

  7. Ex. 5 Find the Area of a Kite • Using your knowledge of area of a triangle, right triangle trigonometry and the Pythagorean Theorem. Find the area and perimeter of the figure below.

  8. Ex. 6 Find the Area of a Trapezoid • Using your knowledge of area of a triangle, right triangle trigonometry and the Pythagorean Theorem. Find the area of the trapezoid below.

  9. Part 2 Areas of Regular Polygons

  10. 7.5 Area of Regular Polygons • A regular polygon has equal sides and equal angles • The radius of the polygon is the distance from the center to a vertex radius center

  11. 7.5 Area of Regular Polygons • Drawing all of the radii will create several congruent, isosceles triangles.

  12. 7.5 Area of Regular Polygons • The apothem is the perpendicular distance from the center to the midpoint of one of the sides. center apothem

  13. 7.5 Area of Regular Polygons • An apothem bisects one of the angles created by two radii, creating another pair of congruent triangles radii apothem

  14. 7.5 Area of Regular Polygons • Example 1: Find the measure of each numbered angle m∠1= m∠2= m∠3= 360∕6 = 60° 60∕2 = 30° 180-90-30=60° 1 2 3

  15. 7.5 Area of Regular Polygons • Example 2: Find the measure of each numbered angle 6 4 5 m∠4= m∠5= m∠6= 360∕8 = 45° 45∕2 = 22.5° 180-90-22.5=67.5°

  16. 7.5 Area of Regular Polygons • Example 3: Find the measure of each numbered angle m∠7= m∠8= m∠9= 360∕5= 72° 72∕2 = 36° 180-90-36=54° 7 8 9

  17. 7.5 Area of Regular Polygons • The area of a regular polygon equals one half the product of the apothem and the perimeter • (Perimeter equals the side length times the number of sides, by the way)

  18. 7.5 Area of Regular Polygons • Example 4: Find the area of the regular polygon 8 in 12.3 in

  19. 7.5 Area of Regular Polygons • Example 5: Find the area of the regular polygon Use Pythagorean Theorem! 18 ft 23.5 ft 21.7 ft 9 ft

  20. 7.5 Area of Regular Polygons • Example 6: Find the area of the regular polygon Use Pythagorean Theorem! 6.1 4.9 3.6 7.2

  21. 7.5 Area of Regular Polygons • Example 7: Find the area of the regular polygon Use shortcut for 30-60-90 triangle! 10 cm 30 10 5√3 60 5

  22. 7.5 Area of Regular Polygons • Example 8: Find the area of the regular polygon Use shortcut for 30-60-90 triangle! 60 4.5 15.6 m 30 7.8

More Related