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• To step
• Method 1 of 2: Calculate the area of ​​which the central angle and radius are known
• Method 2 of 2: Calculate the area with a known arc length and radius

Sometimes it is necessary to determine the area under an arc, or the area of ​​a segment. A segment is part of a circle that is shaped like a slice of pizza or pie. To determine the area of ​​this piece, you need to know the length of the circle's radius. In addition to the radius, you need to know either the central angle in degrees or the length of the arc. In these measurements, determining the area of ​​a segment is a simple matter of filling in the numbers in fixed formulas.

To step

Method 1 of 2: Calculate the area of ​​which the central angle and radius are known

1. Draw up the formula:${ displaystyle A = left ({ frac { theta} {360}} right) pi r ^ {2}}$Enter the central corner of the segment in the formula. Divide the central angle by 360. Doing this will give you the portion or percentage of the entire circle that the segment represents.
   • For example, suppose the central angle is 100 degrees, then you divide 100 by 360 to get 0.28. So the area of ​​the segment is about 28 percent of the area of ​​the whole circle.
   • If you don't know the central angle, but you know which part of the circle the segment is, find the angle by multiplying that fraction by 360. For example, if you know that the segment is one-fourth of the circle, multiply 360 by one-fourth (0.25) to get 90 degrees.
2. Enter the radius in the formula. Square the radius and multiply the answer by 𝝅 (3,14). This calculates the area of ​​the entire circle.
   • For example, if the radius is 5 cm, then you calculate 5 x 5 = 25, then 25 x 3.14 = 78.5.
   • If you don't know the length of the radius, but you know the diameter, divide the diameter by two to find the radius.
3. Multiply the two numbers together. You multiply the percentage again by the area of ​​the entire circle. This will give you the area of ​​the segment.
   • For example: 0.28 x 78.5 = 21.89.
   • Since you are calculating the area, your answer should be expressed in square centimeters.

Method 2 of 2: Calculate the area with a known arc length and radius

1. Draw up the formula:${ displaystyle A = { frac {rl} {2}}}$Enter the arc length and radius in the formula. You are going to multiply these two numbers to get a new counter.
   • For example, if the arc length is 5 cm and the radius is 8 cm, your new counter will be 40.
2. Divide by two. You divide the counter you find in step two. This will give you the area of ​​the segment.
   • For instance: ${ displaystyle { frac {40} {2}} = 20}$.
   • Since you are calculating the area, your answer should be expressed in square centimeters.