Area of Circles and Sectors

Related Topics:
More Lessons for High School Regents Exam
Math Worksheets

Share this page to Google Classroom

High School Math based on the topics required for the Regents Exam conducted by NYSED.

The following diagrams give the formulas for the area of circle and the area of sector. Scroll down the page for more examples and solutions.
Area of Sector

How to Calculate the Area of a Circle?

Area of a circle, how to get the formula
The area of circles is derived by dividing a circle into an infinite number of wedges formed by radii drawn from the center. When these wedges are rearranged, they form a rectangle whose height is the radius of the circle and whose base length is half of the circumference of the circle.

How to Find the Area of a Sector of a Circle?
This video will first show how to identify what fraction of the circle is occupied by the sector and then how to multiply that fraction by the entire area of the circle.

Area of a Sector
A sector in a circle is the region bound by two radii and the circle. Since it is a fractional part of the circle, the area of any sector is found by multiplying the area of the circle, pi × r2, by the fraction x/360, where x is the measure of the central angle formed by the two radii.
This video explains the definition of a sector and how to find the sector area of a circle. It shows how to solve 2 example problems, one for finding the sector of a circle and the other to find the radius of a circle with a given sector area.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.