11.3 Vocabulary Radius of a Regular Polygon Apothem of a Regular Polygon

Perimeter and Area Formulas you should be familiar with…  

NOTE: This area formula works for ANY quadrilateral with perpendicular diagonals

EXAMPLE 1B: Given Rhombus RHOM with a perimeter = 52 and one diagonal length = 24, find the length of the second diagonal and the area of RHOM

The center of a regular polygon is equidistant from the vertices The center of a regular polygon is equidistant from the vertices. The distance from the center to a vertice is called the radius of the polygon. The apothem is the distance from the center to a side. A central angle of a regular polygon has its vertex at the center, and its sides pass through consecutive vertices. Each central angle measure of a regular n-gon = Regular pentagon DEFGH has a center C, apothem BC, central angle DCE and r = CD.

To find the area of a regular n-gon with side length s and apothem a, divide it into n congruent isosceles triangles. area of each triangle: total area of the polygon:

Note: If you draw one of the triangles with the central angle, the apothem, the radius, and the side length you can use the Pythagorean theorem or trigonometry to calculate the missing pieces.

MK = 1.368, LM = 3.759 s = 2(1.368) = 2.736 Nonagon (n = 9) so Perimeter is 9(2.736) = 24.624 A = ½ aP A= ½ (3.759)(24.624) A = 46.3

EXAMPLES: 1. Find the area of a regular octagon with r = 12 and s = 9.2 2. Find the area of a regular pentagon with s = 10

EXAMPLES: 3. Find the area of a regular hexagon with s = 6 4. Find the area of a regular hexagon with a = 10