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Calculating Areas of Regular Polygons and Circles

Learn how to find areas of regular polygons and circles, understand apothems and their usage in polygon areas, calculate apothem area using formulas. Explore examples such as finding the area of a regular hexagon, and learn the formula for finding the area of a circle. Practice problems included.

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Calculating 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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