What is the Formula for the Area of a Sector of a Circle?

What is the Formula for the Area of a Sector of a Circle?

Note:

A sector is just a fraction of the area of a circle. Did you know that there's a formula to help you find the area of a sector? In this tutorial, you'll learn how to find that formula! Take a look!

Keywords:

  • area
  • circle
  • sector
  • area of sector
  • central angle
  • radius
  • n
  • degree

Background Tutorials

  • 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 area of a circle.

      • What is a Circle?What is a Circle?

      What is a Circle?

      Circles are a fundamental part of math! In this tutorial, you'll be introduced to circles and see the different parts of a circle such as the diameter, radius, and chord. Check out this tutorial to learn about circles!

      • What is the Formula for the Area of a Circle?What is the Formula for the Area of a Circle?

      What is the Formula for the Area of a Circle?

      Did you know that you can figure out the formula for the area of a circle by first turning the circle into a parallelogram? It seems a little weird, but it really works! Watch this tutorial to see how it's done!

  • Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

      • What is a Sector and Central Angle?What is a Sector and Central Angle?

      What is a Sector and Central Angle?

      Just about everything in math has a name! Did you know that a fraction of the area of a circle is known as a sector? This tutorial introduces you to the term sector and gives you examples of sectors. Take a look!

Further Exploration

  • Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.