The fan is a figure enclosed by the centre of the circle, two points on the circle and the arc of the circle that does not coincide with these two points, usually the central angle of the fan is greater than 0° but less than 360°, and its area is equal to the proportion of the arc of the circle corresponding to the central angle multiplied by the area of the circle. mathematical-formula.com provides three formulas for calculating the area of a sector, as follows:
2, arc length calculation method:
The third formula used to calculate the area of a sector is S = (1/2)lr, where l is the radius of the sector and r is the arc length of the sector (the arc length is the length of an arc along a circumference). For example, the area of a sector with a radius of 8cm and an arc length of 10cm is S = (1/2)×8×10 = 40 square centimetres.
3, radian of centre calculation method:
The radian of the centre of a circle is calculated by the following formula: S = (|α|r^2)/2, where α is the radian of the centre angle of a circle and r is the radius of a circle. For example, a fan with a radius of 6 cm and a centre angle of π/3 radians has an area of S = (|π/3|×6×6)/2 = 18 square centimetres.
The mathematician Kepler, who had boldly divided the circle into an infinite number of small sectors, boldly claimed that the area of an infinitesimal sector is equal to the area of its corresponding infinitesimal triangle, and that the area of a circle is equal to the sum of the areas of an infinite number of small sectors. This is not a rigorous proof, of course, but there are some ideas about calculus in it.
It should be noted that the centre angle in the sector area formula must be expressed in degrees or radians, and cannot be mixed, and that the sector area formula only applies to the complete sector; if the sector is incomplete, it must be calculated according to the actual situation.
