1 / 15

11-3 Areas of Regular Polygons and Circles

11-3 Areas of Regular Polygons and Circles. Objectives. Find areas of regular polygons Find areas of circles. Find Areas of Regular Polygons. A Definition…. Apothem – a segment that is drawn From the center of a regular polygon Perpendicular to the side of the polygon.

vala
Download Presentation

11-3 Areas of Regular Polygons and Circles

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. 11-3Areas of Regular Polygons and Circles

  2. Objectives • Find areas of regular polygons • Find areas of circles

  3. Find Areas of Regular Polygons

  4. A Definition… Apothem – a segment that is drawn From the center of a regular polygon Perpendicular to the side of the polygon. If all radii were drawn, there would be 6 congruent isosceles triangles. An area of a hexagon is determined by adding areas of the triangles inside. A B H F G C E D

  5. A Formula… • Area of a triangle = ½bh = ½sa If the area of a triangle = ½sa, then the area of a hexagon = 6(½sa)

  6. Example #1… Find the are of a regular pentagon with a perimeter of 40 cm. K P J L P N Q M

  7. TAN angle MPQ = QM / PQ TAN 36 = 4 / PQ PQ = 4 / TAN 36 PQ ~ 5.5 ½ (40)(5.5) = A ~110 So the area of the pentagon is about 110 centimeters.

  8. Find Areas of Circles

  9. Area of a Circle… • Area of a circle = r²

  10. Example #2… A caterer has a 48-inch diameter table that is 34 inches tall. She wants a tablecloth that will touch the floor. Find the area of the tablecloth. 48 in 34in

  11. 34 + 48 + 34 = ll6 divided by 2 = 58 so the radius = 58. • A = pi(58)² • ~ 10,568

  12. Example #3… • Find the area of the shaded region. Assume that the triangle is equilateral. 4m

  13. A = pi(4)² ~ 50.3 – area of circle Use 30-60-90 rules AB = 2 BC = 2√3 DB = 2√3(√3) = 6 A = ½ (4√3)(6) ~20.8 50.3 – 20.8 =29.5 m²

  14. Assignment… • Page 613 • #’s 8 – 23, 26

  15. Questions? Thank you! Laura Beth Stover Connor Reece

More Related