11-5: Areas of Circles and Sectors 11-6: Areas of Regular Polygons Objectives: Find and apply the formula for the area of a circle. Find and apply the formula for regular polygons. Common Core Standards: A-SSE-1, G-C-5, G-GMD-1, G-MG-1, G-MG-3, N-Q-1 A-SSE-1, G-CO-12, G-CO-13, G-MG-1, N-Q-1, N-Q-3

EXAMPLE 1 Find the indicated measure. Area r = 2.5 cm

EXAMPLE 1Find the indicated measure. A = cm 2 Diameter

EXAMPLE 2 Find the areas of the sectors formed by UTV.

GUIDED PRACTICE 1. Area of D Use the diagram to find the indicated measure.

EXAMPLE 3 Use the diagram to find the area of V.

The center of a regular polygon is equidistant from the vertices. 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 is

Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE.

EXAMPLE 1 m AFB In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure.

EXAMPLE 2You are decorating the top of a table by covering it with small ceramic tiles. The table top is a regular octagon with 15 inch sides and a radius of about 19.6 inches. What is the area you are covering?

EXAMPLE 3 A regular nonagon is inscribed in a circle with radius 4 units. Find the perimeter and area of the nonagon.

GUIDED PRACTICE Find the perimeter and the area of the regular polygon.