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Areas
Regular polygon

A regular polygon is apolygon which is equiangular (all angles are congruent) and equilateral (all sides have the same length).

Attributes:

• The sides are the straight line segments that make up the polygon.
• The vertex is a corner of the polygon. In any polygon, the number of sides and vertices are always equal.
• The center is the point inside a regular polygon that is equidistant from each vertex.
• The apothem of a regular polygon is the line from the center to the midpoint of a side.
• The radius is the distance from the center to any vertex.
• By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides.
 Area of a regular polygon: $Area=\frac{P\;\cdot\;a}{2}$ where P is the perimeter and a is the apothem Sometimes you will find a similar formula: $Area=\frac{s\;\cdot\;n\;\cdot\;a}{2}$ where n is the number of sides, s is the length of the each side and a is the apothem.

 Find the area of the regular polygon: $Area=\frac{P\cdot\;a}{2}$ = $\frac{40\;\cdot\;6}{2}$ = $\frac{240}{2}$ = 120 cm2

The lenght of the side of a heptagon is 4 units. The lenght of the apothem is 4.15. Find its area.

Area=