Areasof Regular Polygons

Jonathan DuarteNatalia Saravia

Carolina LorenzaAlejandro Botran

Jorge Juan Samayoa

Apothemof a PolygonApothem 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:

ExamplesofApothems

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.

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.

Example # 1

Example # 2

Example # 3

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

ExamplesExamples:http://www.mathopenref.com/polygoncentralangle.html

Center of thePolygon and Radius of

thePolygonCenter 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

Examples

Examples

n360

n = number of sides

= central angle

725

360

606

360

Size doesn’t matter the angle is always the same