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Understanding Regular Polygons: Construction, Angles, and Area Formulas

A regular polygon is defined by three characteristics: it is convex, all sides are congruent, and all angles are equal. This guide covers the construction of regular polygons, such as hexagons and octagons, using circles and equal spacing. It also delves into the calculations of central, interior, and exterior angles for regular polygons, as well as the area formula based on the apothem and perimeter. Discover how to apply these principles to equilateral triangles and hexagons, enhancing your geometry skills.

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Understanding Regular Polygons: Construction, Angles, and Area Formulas

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Presentation Transcript

  1. 16-2 Regular Polygons

  2. A polygon is regular if (1) it is convex, (2) all of its sides are congruent, and (3) all of its angles are congruent.

  3. Construction of a regular hexagon • Draw a circle and use the length of the radius to mark off 6 equal spaced points then connect the consecutive points

  4. Constructing a regular Octagon Draw a circle. Mark off 8 equal spaced points.

  5. For regular polygons each central angle is 360 n

  6. For regular polygons each interior angle is 180(n-2) n 180-360/n

  7. For regular polygons each exterior angle is 360 n

  8. Apothem -> the segment from the center drawn perpendicular to any of the

  9. Area formula for a regular polygon • A = ½ ap • Area = ½ ( Apothem ) ( Perimeter )

  10. Equilateral triangle s2√3 4

  11. Hexagon 3s2√3 2

  12. Pg. 540(1,4,6-8, 10 (for 5,9,and 15), 11(for 72,45,and 24), 12 (for 140 and 160), 13,14)

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