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# 3.C: Circles - Area, Sector, Circumference, Arc, and Angles

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## Overview

The purpose of this lesson is to learn how to find the area of a circle or a sector and the distance of the circumference or an arc.

This lesson will address the following CCRS Standard(s) for Geometry:

• 7.G.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and the area of a circle
• G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc

## Directions

1. Take notes while watching videos below
2. Go to http://wamap.org and log into our course to complete assignment 3.C with 80% or better.

### Do

Complete assignment 3.C with 80% or better at http://wamap.org

## Summary

In this lesson we have learned:

• A circle is all the points equidistant from a center point
• The area of a circle: </mi> <msup> <mi>r</mi> <mn>2</mn> </msup> [/itex]' data-equation-content="A=\pi r^2">
• The area of a sector of d degrees: </mi> <msup> <mi>r</mi> <mn>2</mn> </msup> [/itex]' data-equation-content="A=\frac{d}{360}\pi r^2">
• The circumference of a circle: </mi> <mi>d</mi> <mo>=</mo> <mn>2</mn> <mi>&#x03C0;</mi> <mi>r</mi> [/itex]' data-equation-content="C=\pi d=2\pi r">
• The distance of an arc of a degrees: </mi> <mi>d</mi> <mo>=</mo> <mfrac> <mi>a</mi> <mn>180</mn> </mfrac> <mi>&#x03C0;</mi> <mi>r</mi> [/itex]' data-equation-content="Arc=\frac{a}{360}\pi d=\frac{a}{180}\pi r">