How to Calculate the Area of a Sector – Step-by-Step Guide and Formula

Area of a sector

The area of a sector is a measurement of the portion of a circle enclosed by two radii and the arc connecting them

The area of a sector is a measurement of the portion of a circle enclosed by two radii and the arc connecting them. It is important to note that a sector is a part of a circle, similar to a slice of pizza.

To calculate the area of a sector, you need to know two things:
1. The measure of the central angle (θ) in degrees or radians.
2. The radius (r) of the circle.

The formula to find the area of a sector is:

Area = (θ/360) × π × r²

Here’s a step-by-step explanation of how to use the formula:
1. Convert the central angle measure from degrees to radians if necessary. To do this, multiply the degree measure by π/180. For example, if the central angle is 45 degrees, multiply 45 by π/180 to get the measure in radians.
2. Square the radius to get r².
3. Multiply θ/360 by π by multiplying the central angle measure in radians by π.
4. Multiply the result from step 3 by r².
5. Round the final answer to the desired level of precision.

Let’s solve an example:
Suppose you have a sector with a central angle of 60 degrees and a radius of 5 units. To find the area of this sector, follow these steps:

1. Convert 60 degrees to radians: 60 × π/180 = π/3 radians.
2. Square the radius: 5² = 25.
3. Multiply π/3 by 25: (π/3) × 25 = (25π)/3 ≈ 26.18 square units.

Therefore, the area of the sector is approximately 26.18 square units.

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