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This geometry math tutorial from NutshellMath offers targeted homework help on finding the area of regular polygons. The instruction is focused on problems 13-18, 33-34 and 44-45 on pages 383 and 384 in the Geometry text from Prentice Hall Mathematics.
A regular polygon is a polygon with all internal angles and sides congruent. It is possible to find the area of any polygon by breaking it down into simpler pieces and using formulas for area for each of the pieces. With regular polygons, however, a single formula can be used.
The area of a regular polygon is equal to one-half the product of the perimeter and the apothem of the polygon. The perimeter is the sum of all the sides, which for a regular polygon is the product of the length of one side and the number of sides. The apothem is the length of a segment from the center of the polygon to the midpoint of one of the sides. The apothem is a perpendicular bisector of the side it intersects.
The problems covered by this tutorial involve finding the area of regular polygons using this formula by first finding either the perimeter or apothem from other information. To find the perimeter or the apothem when only one is known, it is possible to construct right triangles inside the figure, and use trigonometry and known angle measures to solve for the unknown lengths. Often these triangles will be special triangles, such as 45-45-90 or 30-60-60 right triangles, whose side relationships are established. Once the perimeter and the apothem are known, the formula relating the two to area can be used to solve for the area.
This geometry math tutorial from NutshellMath offers targeted homework help on finding the area of regular polygons. The instruction is focused on problems 13-18, 33-34 and 44-45 on pages 383 and 384 in the Geometry text from Prentice Hall Mathematics.
A regular polygon is a polygon with all internal angles and sides congruent. It is possible to find the area of any polygon by breaking it down into simpler pieces and using formulas for area for each of the pieces. With regular polygons, however, a single formula can be used.
The area of a regular polygon is equal to one-half the product of the perimeter and the apothem of the polygon. The perimeter is the sum of all the sides, which for a regular polygon is the product of the length of one side and the number of sides. The apothem is the length of a segment from the center of the polygon to the midpoint of one of the sides. The apothem is a perpendicular bisector of the side it intersects.
The problems covered by this tutorial involve finding the area of regular polygons using this formula by first finding either the perimeter or apothem from other information. To find the perimeter or the apothem when only one is known, it is possible to construct right triangles inside the figure, and use trigonometry and known angle measures to solve for the unknown lengths. Often these triangles will be special triangles, such as 45-45-90 or 30-60-60 right triangles, whose side relationships are established. Once the perimeter and the apothem are known, the formula relating the two to area can be used to solve for the area.