Arc length and sector area worksheet (with answer key)

Many real-world applications involve arc length. If a rocket is launched along a parabolic path, we might want to know how far the rocket travels. Or, if a curve on a map represents a road, we might want to know how far we have to drive to reach our destination.

This worksheet will explain the basics of calculating the arc length and the sector area.

What is arc length?

The interspace between two locations along a portion of a curve is defined as the arc length. A circle’s arc is any section of its circumference. The angle subtended by an arc at any point is the angle created by the two line segments connecting that point to the arc’s endpoints. 

In the circle depicted below, for example, OP is the arc of the circle with centre Q. L denotes the arc length of this OP.

How can we calculate arc length?

The length of an arc may be computed using several formulae dependent on the unit of the arc’s central angle. The centre angle can be measured in degrees or radians, and the arc length of a circle is calculated appropriately. The arc length formula for a circle is times the radius of a circle.

What is the sector area?

The area of a sector is the space inside the section of the circle created by two radii and an arc. It is a fraction of the area of the entire circle.

How will the “Arc length and sector area worksheet with answers” help you?

This worksheet will help you better understand the concept of arc length and sector area. It will challenge the student’s ability to identify them.

Instructions on how to use the “Arc length and sector area worksheet with answers”:

Use this math worksheet you learn about equating the sector area and arc length thoroughly. 

A reflection section is included at the end of this worksheet to assist the student think about their thinking (metacognition) and analyse how they performed in the session.

Finally, it challenges the student to devise their problems and compare them with the ones he/she learned from the worksheet.


This worksheet will help you gain the essential skills to find the area and arc length.

If you have any questions or comments, please let us know.

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