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Example 1

Example 1. Explain how you could find the area of the regular hexagon shown. Regular Inscribed Polygon. The diagram shows a regular polygon inscribed in a circle. Center of circle = center of the polygon Radius of circle = radius of the polygon. Regular Inscribed Polygon.

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Example 1

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  1. Example 1 Explain how you could find the area of the regular hexagon shown.

  2. Regular Inscribed Polygon The diagram shows a regular polygon inscribed in a circle. • Center of circle = center of the polygon • Radius of circle = radius of the polygon

  3. Regular Inscribed Polygon The apothem of the polygon is the distance from the center to any side of the polygon. • Apothem = height of isosceles triangle with 2 radii as legs

  4. Regular Inscribed Polygon A central angle of a polygon is an angle formed by two consecutive radii. • Measure of central angle =

  5. Areas of Regular Polygons Objective: • To find the area of a regular n-gon

  6. Example 2 • Identify the center, a radius, an apothem, and a central angle of the polygon. • Find m<XPY, m<XPQ, m<PXQ.

  7. Example 3 Assume a regular n-gon has a side length of s and an apothem of a. Find a formula for the area of the regular n-gon.

  8. Area of a Regular Polygon The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P.

  9. Regular 3-gon What is the measure of each central angle in an equilateral triangle? What is the measure of the angle formed by the apothem and the radius of the triangle?

  10. Regular 4-gon What is the measure of each central angle in a square? What is the measure of the angle formed by the apothem and the radius of a square?

  11. Regular 5-gon What is the measure of each central angle in a regular pentagon? What is the measure of the angle formed by the apothem and the radius of the pentagon?

  12. Regular 6-gon What is the measure of each central angle in a regular hexagon? What is the measure of the angle formed by the apothem and the radius of the hexagon?

  13. Example 4 Find the area of each regular polygon.

  14. Summary

  15. Example 5 Find the area of each regular polygon.

  16. Example 6 Find the area of each regular polygon.

  17. Example 7 Find a formula for the area of a regular hexagon in terms of s, the side length.

  18. Example 8 The perimeter of a regular hexagon is 48 cm. What is the area of the hexagon?

  19. Challenge Problem Find the area of the shaded region.

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