11-5: Areas of Circles and Sectors11-6: 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 1Find the indicated measure. Area

r = 2.5 cm

EXAMPLE 1Find the indicated measure.

A = 113.1 cm2

Diameter

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

GUIDED PRACTICE

1. Area of D

Use the diagram to find the indicated measure.

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

GUIDED PRACTICEFind the perimeter and the area of the regular polygon.