1. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons 9-2 Developing Formulas for Circles and Regular Polygons Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Warm Up Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse 2 ft 2. a 45°-45°-90° triangle with leg length 4 in. 3. a 30°-60°-90° triangle with longer leg length 3m

3. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Develop and apply the formula for the area of a regular polygon. Develop and apply the formula for the area of a triangle. Objectives

4. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons center of a regular polygon apothem central angle of a regular polygon Vocabulary

5. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons The center of a regular polygon is equidistant from the vertices. The apothem is the distance from the center to a side. A central angle of a regular polygon has its vertex at the center, and its sides pass through consecutive vertices. Each central angle measure of a regular n-gon is

6. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE.

7. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons To find the area of a regular n-gon with side length s and apothem a, divide it into n congruent isosceles triangles. The perimeter is P = ns. area of each triangle: total area of the polygon:

8. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons

9. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Find the area of regular heptagon with side length 2 ft to the nearest tenth. Example 3A: Finding the Area of a Regular Polygon

10. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Example 3B: Finding the Area of a Regular Polygon Find the area of a regular dodecagon with side length 5 cm to the nearest tenth.

11. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Check It Out! Example 3 Find the area of a regular octagon with a side length of 4 cm.

12. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Area of a Triangle given SAS Formula: (1/2) bc (sin A)

13. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Area of a Triangle given SAS Example 4 Find the area of the given triangle

14. Holt Geometry 9-2 Developing Formulas for Circles and Regular Polygons Exit Slip Find the area of each regular polygon to the nearest tenth. 1. a regular nonagon with side length 8 cm A ≈ 395.6 cm 2 2. a regular octagon with side length 9 ft A ≈ 391.1 ft 2 Find the area of the triangle. 3.