A sector of a circle is a section that is bounded by two radii and an arc. It is similar to a slice of a pizza. To calculate the area of a sector of a circle, you need to know two things: the measure of the central angle that defines the sector, and the radius of the circle.

The formula for the area of a sector of a circle is:

A = (θ/360) x πr²

Where A is the area of the sector, θ is the measure of the central angle in degrees, and r is the radius of the circle.

To use this formula, you first need to convert the central angle from degrees to radians. You can do this by multiplying the measure of the angle in degrees by π/180.

For example, if the angle measure is 45 degrees, you would convert it to radians as follows:

45 x (π/180) = 0.7854 radians

Next, you need to square the radius of the circle. For example, if the radius is 5 units, you would square it as follows:

5² = 25

Now you can plug in the values for θ and r into the formula and solve for A:

A = (0.7854/360) x π x 25

A = 0.1374 x 78.54

A = 10.2 square units

So the area of the sector with a central angle of 45 degrees and a radius of 5 units is 10.2 square units.

It’s important to note that the central angle must be measured in degrees, not radians. If you are given the angle measure in radians, you will need to convert it to degrees before using the formula.

Another thing to keep in mind is that the formula only works for sectors of circles, not segments. A segment is a section of a circle that is bounded by a chord and an arc. To calculate the area of a segment, you would need to subtract the area of a triangle that is formed by the two radii and the chord from the area of the sector. This requires a different formula and additional calculations.

In summary, the area of a sector of a circle can be calculated using the formula A = (θ/360) x πr², where A is the area of the sector, θ is the measure of the central angle in degrees, and r is the radius of the circle. To use the formula, you need to convert the angle measure from degrees to radians, square the radius, and plug in the values. It’s important to note that the formula only works for sectors of circles, not segments.

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