How to Calculate the Area of a Sector | Formula, Steps, and Example

Area of a Sector of Circle

The area of a sector of a circle is the portion of the whole circle enclosed by two radii and their intercepted arc

The area of a sector of a circle is the portion of the whole circle enclosed by two radii and their intercepted arc. To calculate the area of a sector, you need to know the measure of the central angle (θ) that the sector subtends at the center of the circle, as well as the radius (r) of the circle.

The formula to find the area of a sector is given by:

Area = (θ/360) * π * r^2

Here, θ/360 represents the fraction of the total angle that the sector occupies. Multiply this fraction by π (pi), which is approximately 3.14159, and then multiply the result by the square of the radius (r^2).

To apply this formula, follow these steps:

1. Determine the measure of the central angle (θ) in degrees.
2. Determine the radius (r) of the circle.
3. Divide the measure of the central angle (θ) by 360 to find the fraction of the whole circle it represents.
4. Multiply this fraction by π and then multiply the result by the square of the radius (r^2).
5. Round the answer to an appropriate number of decimal places or leave it in terms of π if required by the question.

For example, let’s say we have a circle with a radius of 5 units and a central angle of 60 degrees.

1. The measure of the central angle is θ = 60 degrees.
2. The radius of the circle is r = 5.
3. The fraction of the whole circle occupied by the sector is θ/360 = 60/360 = 1/6.
4. Multiply this fraction by π and then multiply the result by the square of the radius: (1/6) * π * (5^2) = (1/6) * π * 25 = (25/6) * π.
5. The area of the sector is approximately 13.09 square units (rounded to two decimal places) or (25/6)π square units in terms of π.

Remember to always check if the units of measurement match and round the answer appropriately according to the instructions or context of the problem.

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