Area of a Sector

Area of a Sector

Objective

• Identify the formula of for finding the area of a sector

• Solve for the area of a sector

Area of a Circle & Semicircle

Area of a full circle:  $\pi r^2$  
  Area of a semi-circle:   $\frac{1}{2}\pi r^2$  

Area of a Quarter-Circle

Area of a Quarter-circle = $\frac{1}{4}\pi r^2$  

If I want to find the area of an part of a circle, how would I do it?

Area of a Sector

• Area is a fractional part of a circle

•  To find the area of a sector:  $\left(\frac{n}{360}\right)\pi r^2$  

• n = degrees of the central angle of the sector

• r=radius

Example 1:

• Find the area of a sector with a central angle of $40\degree$   and a radius of 12 cm. 

• Area of Sector = $\frac{n}{360}\pi r^2$  

• n= 40 & r=12

• AoS= $\frac{40}{360}\pi\ 12^2$  

• AoS= $\frac{144}{9}\pi$  or  $50.27cm^2$  

Example 2

• A pizza has a diameter of 12 inches and is cut into 10 equal slices. Find the area of a pizza slice, rounded to the nearest hundredth.

• n= $\left(\frac{360}{10}\right)$  = $36\degree$  & r= $\frac{12}{2}$  =6

• Area of 1 slice:  $\frac{36}{360}\pi6^2$  

• =11.309733

Multiple Choice

Find the area of a sector with a radius of 9ft and an angle measure of  $132\degree$  

•  $10.27ft^2$  

•  $93.31ft^2$  

•  $29.7ft^2$   

•  $85ft^2$  

Fill in the Blank

Find the area of the sector shown. Round to the nearest hundredth

Multiple Choice

What is the area of the shaded sector?

• $6.56yd^2$

• $7.49yd^2$

• $8.72yd^2$

Fill in the Blank

Find the central angle of the sector of the circle with a radius of 12 ft and a sector area of 72  $ft^2$  

Multiple Choice

What is the formula for finding the area of a sector. 

• $\left(\frac{n}{360}\right)\pi r^2$

• $2\pi r$

• $\pi r^2$