1 / 13

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.

moses-barnett
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 area of a regular pentagon with a perimeter of 40 cm. K P J L P N Q M

  7. We first need to find the apothem. Since it is regular, all of the central angles are congruent, or equal to 360/5 or 72°. That makes angle NPQ equal to 36°. Side NM = 8 since the perimeter is 40, so NQ = 4. Now, we can solve the problem: tan NPQ = QN / PQ tan36 = 4 / PQ PQ = 4 / TAN 36 PQ = 5.5 Area = ½ Pa or ½ (40)(5.5) = 110 So the area of the pentagon is 110 cm. K P J L P N Q M

  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. 34 + 48 + 34 = ll6 divided by 2 = 58 so the radius = 58. A = pi(58)² = 10,568 inches2 48 in 34in

  11. Example #3… Find the area of the shaded region. Assume that the triangle is equilateral and the radius of the circle is 4. 4m

  12. A = pi * r² A = pi(4)² = 50.3  Area of Circle Construct ΔABC, a right Δ . Use 30-60-90 rules to find the lengths of the sides and then to find the height of the equilateral triangle. AB = 2 BC = 2√3 DB = 2√3(√3) = 6  Height of ΔCDE One side of ΔCDE is equal to 2(2√3) = 4√3 So, A = ½ (4√3)(6) = 20.8  Area of ΔCDE Now, area of shaded region is 50.3 – 20.8 which is equal to 29.5 m². D A E B C 4m

  13. Assignment… • Pre-AP Pg. 613 #8 – 22, 24, 30, 32, 39 - 44 • Geometry Pg. 613 #8 – 22, 24, 30, 32, 39 - 41

More Related