1. Agenda  1 st block  45-45-90 and 30-60- 90 triangle worksheet  Notes 11-4  Classwork due by end of class  3 rd block  Pop quiz  Go over homework from Wednesday night  Notes 11-4  Classwork due by end of class

2. Areas of Regular Polygons 11-4

3. Goals/Purpose At the completion of the lesson, you will be able to… identify and calculate the center, radius, apothem, and central angle of a regular polygon Calculate the area of a regular polygon We are studying this material because regular polygons are common in structures and buildings

4. Definitions Center – the center of the circle circumscribed about the polygon radius – a segment drawn from the center of a polygon to a vertex apothem – a segment drawn from the center of a polygon that is perpendicular to a side central angle – an angle formed by two radii drawn to consecutive vertices

5. Theorem 11.6 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 aP, or A = ½ a ns. NOTE: In a regular polygon, the length of each side is the same. If this length is (s), and there are (n) sides, then the perimeter P of the polygon is n s, or P = ns The number of congruent triangles formed will be the same as the number of sides of the polygon.

6. More... 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 divide 360° by the number of sides to find the measure of each central angle of the polygon. 360/n = central angle

7. Ex: Finding the area of a regular polygon A regular pentagon with radius 1 unit. Find the area of the pentagon. B C A 1 1 D

8. Solution: you must find the apothem (or if the apothem was given, you must find the radius, etc) You need to find measure of central angle.  ABC is 360°/5, or 72°.

9. Solution: Draw the apothem. It is an isosceles triangle so it bisects the angle. You now have a right triangle and can use trig ratios to find the missing sides 36 °

10. Solution

11. You try….. Find the area of a regular polygon with 9 sides and a radius of 10

12. Homework Page 442 1-8