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Area of Regular Polygons

Area of Regular Polygons. Brett Solberg AHS ‘11-’12. Warm-up. 1) What is the measure of an interior angle in a regular hexagon? hint (n-2)*180 2) Find the value of x and y in the regular triangle. Which HW problems should we review?. Today’s Agenda. Mini-Quiz Area of Regular Polygons

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Area of Regular Polygons

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  1. Area of Regular Polygons Brett Solberg AHS ‘11-’12

  2. Warm-up • 1) What is the measure of an interior angle in a regular hexagon? hint (n-2)*180 • 2) Find the value of xand y in the regular triangle. • Which HW problems should we review?

  3. Today’s Agenda • Mini-Quiz • Area of Regular Polygons • finding interior angles • finding angles created by radii • using apothem • applying properties of special right triangles • Announcements • 4th Quarter Change – Only one retake for the quarter

  4. Regular Polygon • What is a polygon? • an enclosed figure with at least 3 straight sides. • What is a regular polygon? • a polygon where all the sides and angles are congruent

  5. Radius and Apothem • Any regular polygon can be circumscribed. • Radius: distance from the center to the vertex. • Apothem: perpendicular distance from the center to a side. • Draw and label the other radii and apothems.

  6. Area of a Regular Polygon • The area of a regular polygon is half the product of the apothem and the perimeter. • How do we find perimeter? • p = ns • n= number of sides • s = length of one side

  7. Example 1 • Find the area of a regular decagon with a 12.3 inch apothem and a side length of 8. • Decagon = • Perimeter = • Area =

  8. Example 2 • Find the area of a regular polygon with twenty 12 inch sides and a 37.9 inch apothem. • Perimeter = • Area =

  9. Area of a Polygon • What if we aren’t given the apothem? • fill in missing angles • use properties of special right triangles 30 60

  10. Equilateral Triangle • Label the radii and apothems. • What angles do they create?

  11. Square • Label the radii and apothems. • What angles do they create?

  12. Example 1 – Regular Pentagon • Label the radii and apothem • Find the angles in the regular pentagon.

  13. Regular Hexagon • Label the radii and apothem • Find the angles in the regular pentagon.

  14. Example 3 • Find the area of a regular triangle with a side of 8 inches. in

  15. Example 4 • Find the area of a square with the radius of 8 cm. 8 cm

  16. Homework • 10-3 Worksheet

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