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Mathematics LibreTexts

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

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    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


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


    Complete assignment 3.C with 80% or better at


    In this lesson we have learned:

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