# Area of Sectors and Segments Worksheets

What is the Area of Sectors and Segments of a Circle? Circles are the most common and widely used of all the shapes. They have many features that are useful in many situations; for example, a wheel was one of the first simple machines that made the heavy work of transporting heavy load for humans a lot easier. A circle has a radius which is the distance from its center to the circumference, a diameter that is double the value of the radius, its outer boundary is called the circumference. A chord is any line drawn within a circle that starts from one point on the circumference and extends to another point on the circumference. Sectors in a circle are the area occupied by two radii extended in different directions to the circumference and forming a slice of the circle. Segments, on the other hand, are areas enclosed between a part of the circumference and a chord. To find the area of a sector, you just need to multiply the square of the radius of that circle with the angle in radians subtended in the middle of the circle by that sector and divide the product by two. To find the area of a segment, you first find the area of that sector, then draw a chord in that sector, which then creates a triangle in that sector. Calculate the area of that triangle and subtract it from the area of the sector, and you will get the area of the segment.

• ### Basic Lesson

Guides students through finding arc length and angle. In circle O, the radius is 235, and the measure of minor arc PQ is 200 degrees. Find the length of minor arc PQ to the nearest integer.

• ### Intermediate Lesson

Demonstrates how to find circumference and radius of circle segments. In a circular track the angle is 120 degrees. And the length of minor arc AB is 420. Find the radius of the circle.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of the Area of Sectors and Segments. Find the area of shaded sector shown in fig. The radius of the circle is 12 units and the length of the arc measures 115 units.

• ### Independent Practice 2

Students use Area of Sectors and Segments in 20 assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Area of Sectors and Segments.

• ### Skill Quiz

This tests the students ability to understand Area of Sectors and Segments.

Answers for all lessons and independent practice.

Answers for homework and quiz sheets.

• ### Basic Lesson

Guides students through finding the measure of area of sectors and segments within circles by using given point of reference. In circle O, the radius is 235, and the measure of minor arc PQ is 200 degrees. Find the length of minor arc PQ to the nearest integer.

• ### Intermediate Lesson

Demonstrates how to the circumference and radius of an arc based on segments.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of the Circles: Area of Sectors and Segments.

• ### Independent Practice 2

Students determine the Circles: Area of Sectors and Segments in 20 assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Circles: Area of Sectors and Segments.

• ### Skill Quiz

This tests the students ability to understand Circles: Area of Sectors and Segments.