Understanding Areas of Regular Polygons

Explore the definitions, formulas, and theorems related to regular polygons, including central angles, apothems, and perimeter calculations. Learn how to find the area of a regular polygon through examples and solutions.

• Regular polygons
• Area formulas
• Central angles
• Theorems
• Geometry

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1. Areas of Regular Polygons 10-3

2. Honors On a sheet of warm up paper: Write the name of your podcast group members (don t write your own name) Rate each member from 1-10, 10 being very helpful

3. Area Formulas Rhombus: .5(D1)(D2) Trapezoid: .5(h)(b1+b2) Kite: There ain t one, use your common sense!

4. Definitions center Central angle 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 The number of congruent triangles formed will be the same as the number of sides of the polygon. A = aP, or A = 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

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. C 1 B D 1 A

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 . B 1 C A D

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 B 36 1 C A D

10. Solution B 1 C A D

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