# 8.5: Sector Area

**At Grade**Created by: CK-12

## Learning Objectives

- Calculate the area of a
*sector.*

## Area of a Sector

A **sector** is a section of a circle. Think of it like a pie slice: it is a section bounded on two sides by radii and one side by an arc. The tip of a sector is at the center of the circle:

image from http://en.wikibooks.org/wiki/Geometry/Circles/Sectors

- A
**sector**is just like a slice of ________________ or pizza.

The *area* of a **sector** is simply an appropriate fractional part of the area of the circle.

Suppose a **sector** of a circle with radius and circumference has an arc with a degree measure of and an arc length of units.

- The sector is of the circle.
- The sector is also of the circle.

To find the *area* of the **sector,** just find one of these fractional parts of the *area* of the *circle.* We know that the *area* of the *circle* is . Let be the *area* of the **sector:**

Also,

**Area of a Sector**

A circle has radius . A sector of the circle has an arc with degree measure and arc length units. The area of the sector is square units:

This means that the *area* of a **sector** is one-half of the product of the ________________ and the arc length.

**Example 1**

*Mark drew a sheet metal pattern made up of a circle with a sector cut out. The pattern is made from an arc of a circle and two perpendicular 6 inch radii like so:*

*How much sheet metal does Mark need for the pattern?*

The cut-out **sector** has a **degree measure** of because the radii are *perpendicular*.

The measure of the arc of the metal piece is (the entire circle) – (the cut-out sector) or :

Using the values radius _________ and arc degree measure ,

The *area* of the sector

**Reading Check:**

*Explain the following statement in your own words:*

The area of a sector is a fraction of the area of a circle, and the fraction is calculated by the degree measure of the sector divided by .

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