Section 11-2 Areas of Regular Polygons

Area of an Equilateral Triangle The area of an equilateral triangle is one fourth the square of the length of the side times Formula: or

Given any regular polygon, you can circumscribe a circle about it.

Parts of a Regular Polygon:

Center is the center of the circumscribed circle Example:

Radius is the distance from the center to a vertex Example:

apothem is the (perpendicular) distance from the center of the polygon to a side. Example:

Central angle is an angle formed by two radii drawn to consecutive vertices. Example:

To find the Measure of a Central Angle of a Regular Polygon: **n = the number of sides = Central Angle

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To find the area of any regular n-gon: 1.Divide the polygon into congruent triangles 2.Find the area of one of those triangles 3.Multiply that triangle’s area by the number of triangles that are in the polygon

Area of a regular polygon The area of a regular polygon is equal to half the product of the perimeter and the apothem. Formula: