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11.3 Areas of Regular Polygons and Circles

11.3 Areas of Regular Polygons and Circles. What W e Will Learn. How to find areas of regular polygons. How to find areas of circles. What a apothem is. A pothem.

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11.3 Areas of Regular Polygons and Circles

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  1. 11.3 Areas of Regular Polygons and Circles

  2. What We Will Learn • How to find areas of regular polygons. • How to find areas of circles. • What a apothem is.

  3. Apothem • Apothem is a segment that is drawn from the center of a regular polygon to one of the sides and makes a right angle with that side. Apothem

  4. Area using apothem Area = ½ perimeter x apothem A=1/2 Pa 7 What is the area of regular hexagon ABCDEF? 6 A=126

  5. How to find Apothem The central angles of a regular polygon are congruent. So in the hexagon each measure is 360/6 or 60 degrees. OG also bisects angle AOB So angle AOG is 30 degrees. 8

  6. How to find Apothem Since each side of the hexagon is 8, AG=4 then use trigonometric ratios to find the length of segment OG. Find length of segment OG. 8 OG =6.9

  7. Area of a circle A= π r²

  8. Try this Find the area of the shade region if FD is a radius and hexagon ABCDE is a regular hexagon. C 5 A F B 6 D E Area = 75 square units

  9. Homework Pg 613/ 8-22 all,24-32 evens, 39-44 all omit 28

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