Areasof Regular Polygons

1. Areasof Regular Polygons Jonathan Duarte Natalia Saravia Carolina Lorenza Alejandro Botran Jorge Juan Samayoa

3. Apothemof a Polygon • Apothem of a Polygon= the distance from the center of a polygon to any side of the polygon. • The apothem is the height of the triangle between the center and two consecutive vertices of the polygon. An apothem can also be referred to as the distance of the green segment shown in the picture below. • APOTHEM OF A HEXAGON:

4. ExamplesofApothems

6. Area of a regular Polygon • To find an Area of a Regular polygon you must follow this equation:  • A= 1/2aP • On the next slide I wills how you what does this variable means.

7. Whatdoes a and p stands for? • You might be wondering what does a and P stand for. Well the answer is pretty simple, A stands for the apothem which is similar to the radius;  the distance between the center of a polygon to any side. P stand for perimeter, and as you may remember the perimeter is  the distance around the area. You just have to substitute the values of the given shape into the formula. After you get a and P substitute their values into the equation and then solve, in order to get the Area.

8. Example # 1

9. Example # 2

10. Example # 3

11. Central Angle of a Polygon •  The central angle of a polygon is an angle made by two consecutive vertices in a regular polygon. • All central angles added up = 360. So the formula is 360 divided by the number of sides. •  Central angle = where “n” means number of sides

12. Examples • Examples: • http://www.mathopenref.com/polygoncentralangle.html

13. Center of thePolygon and Radius of thePolygon • Center of the polygon: equidistant point from the vertex to all the corners of the polygon.Radius of the polygon: the distance from the center of a polygon to any vertex

14. Examples

15. Examples

16. = central angle n = number of sides

17. Sizedoesn’tmattertheangleisalwaysthesame