1. 11.2 Areas of Regular Polygons Unit IIIH Day 2

2. Do Now What are the two formulas for a 30º-60º-90º triangle? ▫hypotenuse = _________ ▫long leg = __________ If the hypotenuse = x, label the other two sides in terms of x. x

3. Formula for area of equilateral triangle A = ½ bh…

4. Theorem 11.3 Area of an equilateral triangle The area of an equilateral triangle is one fourth the square of the length of the side times √3 A = ¼ s 2 ss s

5. Ex. 2: Finding the area of an Equilateral Triangle Find the area of an equilateral triangle with 8- inch sides.

6. Vocab The center of the polygon and radius of the polygon are the center and radius of its circumscribed circle, respectively. The apothem is the height of a triangle between the center and two consecutive vertices of a polygon. Hexagon ABCDEF with center G, radius GA, and apothem GH

7. Apothem and Area of Regular Polygons A = Area of 1 triangle # of triangles

8. Theorem 11.4 Area of a Regular Polygon The area of a regular n-gon with side lengths s is half the product of the apothem (a) and the perimeter (P). ▫So A = ½ a  P, or A = ½ a n  s.

9. Vocab. A central angle of a regular polygon is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon. You can find the measure of each central angle of the regular polygon by ________________ ▫ 360º / n = central angle

10. Ex. 3: Finding the area of a regular polygon A regular pentagon is inscribed in a circle with radius 1 unit. Find the area of the pentagon.

11. Ex. 3A A regular octagon is inscribed in a circle with radius 4 centimeters. Find the area of the octagon.

12. Ex. 4: regular dodecagon The enclosure on the floor underneath the Foucault Pendulum at the Houston Museum of Natural Sciences in Houston, Texas, is a regular dodecagon with side length of about 4.3 feet and a radius of about 8.3 feet. What is the floor area of the enclosure?

13. Foucault Pendulum

14. Closure You are given the radius of a regular polygon. Describe how you would find its area.