Area Of Sector
The area of a sector is a measurement of the region enclosed by an arc and two radii of a circle
The area of a sector is a measurement of the region enclosed by an arc and two radii of a circle. To calculate the area of a sector, you need to know the angle (in radians) subtended by the sector at the center of the circle and the radius of the circle.
The formula for the area of a sector is derived from the formula for the area of a circle. The area of a sector can be found using the following formula:
Area = (θ/2) * r^2
Where:
– θ (theta) is the angle (in radians) subtended by the sector at the center of the circle
– r is the radius of the circle
To use this formula, follow these steps:
1. Convert the angle measure from degrees to radians if necessary. Since the formula requires the angle in radians, if the angle is given in degrees, you need to convert it. To convert from degrees to radians, use the following formula:
Radians = (π/180) * degrees
2. Plug in the values into the formula. Substitute the converted angle (in radians) and the radius of the circle into the formula for the area of a sector.
3. Simplify and calculate the area. Multiply the angle (in radians) by the square of the radius, and divide the result by 2. This will give you the area of the sector in square units.
It’s important to note that when using this formula, the angle provided should always be the measure of the angle of the arc that constitutes the sector, not the total angle at the center of the circle.
Remember to use the appropriate units for your calculations (if given) and to round the final answer to the desired level of precision.
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