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Circle math Circumference of a circle Solving equations Law of sines Law of cosines Rounding Square rootHere you will learn how to calculate the area of a sector including how to identify a sector of a circle, form and use the formula for the area of a sector of a circle, and calculate the area of a sector in various scenarios.
Students will first learn about the area of a sector as part of geometry in high school.
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.
Major sector: a major sector has a central angle which is more than katex is not defined
Minor sector: a minor sector has a central angle which is less than katex is not defined
Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents. 40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!
DOWNLOAD FREEPrepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents. 40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!
DOWNLOAD FREEIn order to find the area of a sector, you need to be able to find the area of a circle.
This is because the area of a sector is part of the total area of the circle.
‘How much’ of the circle is decided by the angle created by the two radii.
The sum of the angle around a point is equal to katex is not defined therefore the area of a sector is the fraction of the full circle’s area.
The angle is out of katex is not defined or katex is not defined where katex is not defined (theta) represents the angle, so you can multiply this by the area of the circle to calculate the area of a sector.
To calculate the area of a sector, use the following formula:
katex is not defined
katex is not defined – angle of the sector
katex is not defined – radius of the circle
How does this relate to high school math?
To find the area of a sector:
Calculate the area of the segment shown below.
Give your answer to the nearest thousandth.
Radius: katex is not defined
2Find the size of the angle creating the sector katex is not defined
Angle: katex is not defined (shown by the symbol of the right angle).
3Substitute known values into the formula for the area of a sector and solve.
katex is not definedCalculate the area of the semicircle shown below.
Give your answer in terms of katex is not defined
Determine the length of the radius katex is not defined
Diameter: katex is not defined
Radius: katex is not defined
Find the size of the angle creating the sector katex is not defined
Angle: katex is not defined (the angle in a semicircle is katex is not defined)
Substitute known values into the formula for the area of a sector and solve.
Calculate the area of the sector shown below.
Give your answer to the nearest tenth.
Determine the length of the radius katex is not defined
Radius: katex is not defined
Find the size of the angle creating the sector katex is not defined
Substitute known values into the formula for the area of a sector and solve.
katex is not defined is a sector of a circle.
The length of the radius katex is not defined is katex is not defined
The length of a chord katex is not defined is katex is not defined
Calculate the area of the sector katex is not defined below.
Give your answer to the nearest hundredth.
Determine the length of the radius katex is not defined
Radius: katex is not defined
Find the size of the angle creating the sector katex is not defined
In this example, you are not given the angle of the sector, you need to calculate it first.
Here, you can use the triangle created by the two radii and the chord to find the angle (see below).
In this example, you need to apply the cosine rule to find the angle.
katex is not defined
katex is not defined is the angle you are trying to find, labeled katex is not defined You can therefore use the rearranged cosine rule to find the angle.
katex is not defined
As katex is not defined and katex is not defined
The size of the angle creating the sector is katex is not defined.
Substitute known values into the formula for the area of a sector and solve.
In order to determine missing angle or radius given the area of a sector:
The sector below has an area of katex is not defined
Calculate the length of katex is not defined
Give your answer to the nearest hundredth.
Clearly state which of the properties you know (radius/angle of sector, area of sector).
Radius: katex is not defined
Angle of sector: katex is not defined
Area of sector: katex is not defined
Substitute known values into the formula for the area of a sector.
Solve for the unknown value.
Divide each side of the equation by the fraction.
katex is not defined
Divide each side of the equation by katex is not defined
katex is not defined
Square root each side of the equation to find katex is not defined
katex is not defined
katex is not defined
The sector below has an area of katex is not defined
Calculate the length of katex is not defined
Give your answer to the nearest hundredth.
Clearly state which of the properties you know (radius/angle of sector, area of sector).
Radius: katex is not defined
Angle of sector: katex is not defined
Area of sector: katex is not defined
Substitute known values into the formula for the area of a sector.
Divide both slides by katex is not defined.
katex is not defined
Divide both slides by katex is not defined.
katex is not defined
Multiply both slides by katex is not defined.
katex is not defined
katex is not defined
1. Calculate the area of this sector in terms of katex is not defined
2. Calculate the area of this semicircle in terms of katex is not defined
Since this is a semicircle, you know the angle measure is katex is not defined
katex is not defined
3. Calculate the area of the sector. Round your answer to the nearest tenth.
katex is not defined
4. Calculate the area of this sector. Write your answer to the nearest hundredth.
5. The area of the sector is katex is not defined and the angle katex is not defined
Determine the radius of the sector to the nearest hundredth.
6. katex is not defined is a sector of a circle where katex is not defined and katex is not defined are two ends of the arc of the sector, and katex is not defined is the center. The chord katex is not defined and the radius katex is not defined Calculate the area of the sector to katex is not defined significant figures.
Use the cosine rule to determine the size of angle katex is not defined
katex is not defined rearranges to become katex is not defined
Here, katex is not defined
katex is not defined
Substitute the values of the radius katex is not defined and the angle katex is not defined into the formula for the area of a sector:
katex is not defined
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.
To find the area of a sector, you can use the area formula for a sector of a circle. Area of a sector formula katex is not defined
The area of a sector measures the space inside the sector, while the perimeter of a sector measures the distance around the sector, including the arc and the two radii.
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Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
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