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Areasof Regular Polygons
Jonathan DuarteNatalia Saravia
Carolina LorenzaAlejandro Botran
Jorge Juan Samayoa
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:
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
Examples
Examples:
http://www.mathopenref.com/polygoncentralangle.html
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
Examples
Examples
n
360
n = number of sides
= central angle
725
360
606
360
Size doesn’t matter the angle is always the same