How to Calculate the Area of a Sector
Set up the formula A=(θ360)πr2{\displaystyle A=\left({\frac {\theta }{360}}\right)\pi r^{2}}., Plug the sector’s central angle measurement into the formula., Plug the radius measurement into the formula., Multiply the two numbers together.
Step-by-Step Guide
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Step 1: Set up the formula A=(θ360)πr2{\displaystyle A=\left({\frac {\theta }{360}}\right)\pi r^{2}}.
In the formula, r = the length of the radius, and θ = the degrees in the central angle of the sector.
Remember, the area of a circle is πr2{\displaystyle \pi r^{2}}.
When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents.A circle is 360 degrees, so when you place the measurement of the sector’s central angle over 360, it gives you the fraction of the whole circle. -
Step 2: Plug the sector’s central angle measurement into the formula.
Divide the central angle by
360.
Doing this will give you what fraction or percent of the entire circle the sector represents.
For example, if the central angle is 100 degrees, you will divide 100 by 360, to get
0.28. (The area of the sector is about 28 percent of the area of the whole circle.) If you don't know the measurement of the central angle, but you know what fraction of the circle the sector is, determine the measurement of the angle by multiplying that fraction by
360.
For example, if you know the sector is one-fourth of the circle, multiply 360 by one-fourth (.25) to get 90 degrees. , Square the radius, and multiply it by 𝝅 (3.14).
Doing this will allow you to calculate the area of the whole circle.
For example, if the radius is 5 cm, you will square 5 to get 25, and then multiply 25 by
3.14, to get
78.5.
If you don't know the length of the radius, but you know the diameter, simply divide the diameter by 2 to find the radius. , Again, you will be multiplying the percent by the area of the whole circle.
This gives you the area of the sector.
For example,
0.28 x
78.5 =
21.89.
Since you are finding the area, the answer will be in square centimeters. -
Step 3: Plug the radius measurement into the formula.
-
Step 4: Multiply the two numbers together.
Detailed Guide
In the formula, r = the length of the radius, and θ = the degrees in the central angle of the sector.
Remember, the area of a circle is πr2{\displaystyle \pi r^{2}}.
When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents.A circle is 360 degrees, so when you place the measurement of the sector’s central angle over 360, it gives you the fraction of the whole circle.
Divide the central angle by
360.
Doing this will give you what fraction or percent of the entire circle the sector represents.
For example, if the central angle is 100 degrees, you will divide 100 by 360, to get
0.28. (The area of the sector is about 28 percent of the area of the whole circle.) If you don't know the measurement of the central angle, but you know what fraction of the circle the sector is, determine the measurement of the angle by multiplying that fraction by
360.
For example, if you know the sector is one-fourth of the circle, multiply 360 by one-fourth (.25) to get 90 degrees. , Square the radius, and multiply it by 𝝅 (3.14).
Doing this will allow you to calculate the area of the whole circle.
For example, if the radius is 5 cm, you will square 5 to get 25, and then multiply 25 by
3.14, to get
78.5.
If you don't know the length of the radius, but you know the diameter, simply divide the diameter by 2 to find the radius. , Again, you will be multiplying the percent by the area of the whole circle.
This gives you the area of the sector.
For example,
0.28 x
78.5 =
21.89.
Since you are finding the area, the answer will be in square centimeters.
About the Author
Jeffrey Murray
Creates helpful guides on lifestyle to inspire and educate readers.
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