(1) Arc length calculation formula
Arc length formula
L = n (center angle) * Ï€ (pi) * r (radius)/180
Note: n is the number of center angles, r is the radius, and l is the center angle arc.
In a circle with radius R, because the arc length of the 360Â° central angle is equal to the circle length C=2Ï€R, the arc length of the nÂ° circle angle is l=nÂ°Ï€RÃ·180Â°.
(2) Area calculation of sector
The fan shape is an important figure related to the circle, its area is related to the central angle (vertical angle), the radius of the circle, the central angle is nÂ°, and the radius of the sector area of â€‹â€‹r is n/360*Ï€r^2. If the vertex angle is in radians, it can be simplified as 1/2Ã—radÃ—radius squared.
The fan shape also has similarities with the triangle. The simplified area formula can also be seen as: 1/2 Ã— arc length Ã— radius, similar to the triangle area: 1/2 Ã— bottom Ã— height.
Formula S fan = (lR)/2 (l is fan arc length)
S fan=(n/360)Ï€R^2 (n is the angle of the center angle, R is the radius of the bottom circle)
S fan = (Î±R^2)/2 (Î± is the central angle radians)
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