Difference between revisions of "Find the Area of Regular Polygons"
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== Steps == | == Steps == | ||
===Calculating the Area=== | ===Calculating the Area=== | ||
| − | #Calculate the perimeter. The perimeter is the combined length of the outline of any two-dimensional figure. For a regular polygon, it can be calculated by multiplying the length of one side by the number of sides (''n'').<ref>http://www.mathplanet.com/education/pre-algebra/inequalities-and-one-step-equations/calculating-the-area-and-the-perimeter</ref> | + | #Calculate the perimeter. The perimeter is the combined length of the outline of any two-dimensional figure. For a regular polygon, it can be calculated by multiplying the length of one side by the number of sides (''n'').<ref name="rf1">http://www.mathplanet.com/education/pre-algebra/inequalities-and-one-step-equations/calculating-the-area-and-the-perimeter</ref> |
#Determine the apothem. The apothem of a regular polygon is the shortest distance from the center point to one of the sides, creating a right angle. This is a little trickier to calculate than the perimeter. | #Determine the apothem. The apothem of a regular polygon is the shortest distance from the center point to one of the sides, creating a right angle. This is a little trickier to calculate than the perimeter. | ||
#*The formula for calculating the length of the apothem is this: the length of the side (''s'') divided by 2 times the tangent (tan) of 180 degrees divided by the number of sides (''n''). | #*The formula for calculating the length of the apothem is this: the length of the side (''s'') divided by 2 times the tangent (tan) of 180 degrees divided by the number of sides (''n''). | ||
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#*Note as well, there are no parenthesis in the "Area" equation, so 8.66 divided by 2 multiplied by 60, will give you the same result, just as 60 divided by 2 multiplied by 8.66 will give you the same result. | #*Note as well, there are no parenthesis in the "Area" equation, so 8.66 divided by 2 multiplied by 60, will give you the same result, just as 60 divided by 2 multiplied by 8.66 will give you the same result. | ||
===Understanding the Concepts in a Different Way=== | ===Understanding the Concepts in a Different Way=== | ||
| − | #Understand that a regular polygon can be thought of as a collection of triangles. Each side represents the base of a triangle, and there are as many triangles in the polygon as there are sides. Each of the triangles are equal in base length, height, and area.<ref>http://www.mathsisfun.com/geometry/regular-polygons.html</ref> | + | #Understand that a regular polygon can be thought of as a collection of triangles. Each side represents the base of a triangle, and there are as many triangles in the polygon as there are sides. Each of the triangles are equal in base length, height, and area.<ref name="rf2">http://www.mathsisfun.com/geometry/regular-polygons.html</ref> |
| − | #Remember the formula for the area of a triangle. The area of any triangle is 1/2 times the length of the base (which, in the polygon, is the length of a side) multiplied by the height (which is the same as the apothem in regular polygon).<ref>http://geomalgorithms.com/a01-_area.html</ref> | + | #Remember the formula for the area of a triangle. The area of any triangle is 1/2 times the length of the base (which, in the polygon, is the length of a side) multiplied by the height (which is the same as the apothem in regular polygon).<ref name="rf3">http://geomalgorithms.com/a01-_area.html</ref> |
| − | #See the similarities. Again, the formula for a regular polygon is 1/2 times the apothem multiplied by the perimeter. The perimeter is just the length of one side multiplied the by the number of sides (''n''); for a regular polygon, ''n'' also represents the number of triangles that make up the figure. The formula, then, is nothing more than the area of a triangle multiplied by the number of triangles in the polygon.<ref | + | #See the similarities. Again, the formula for a regular polygon is 1/2 times the apothem multiplied by the perimeter. The perimeter is just the length of one side multiplied the by the number of sides (''n''); for a regular polygon, ''n'' also represents the number of triangles that make up the figure. The formula, then, is nothing more than the area of a triangle multiplied by the number of triangles in the polygon.<ref name="rf2" /> |
== Tips == | == Tips == | ||
