Derivation of the formula of sector area, in our life, we have been studying mathematics. A figure surrounded by an arc and two radii passing through both ends of the arc is called a sector. The formula for calculating the sector area is something we need to learn. Below, I sorted out the formula derivation of sector area for your reference!

Derivation of sector area formula 1

1 region

R is the radius of the sector, n is the degree of the central angle of the arc, π is pi, and L is the arc length corresponding to the sector.

You can also divide the area of the circle where the sector is located by 360 and multiply it by the angle n of the central angle of the sector, as shown below:

Sector area S= angle of central angle (angle system) × pi 3. 14× radius r/360.

(l is arc length and r is sector radius)

Sector area S= arc length L× radius /2

2 derivation process

Deduction process: S=πR×L/2πR=LR/2.

Sector area S= pi 3. 14× radius r× arc length L/2× pi 3. 14× radius = arc length L× radius /2.

(L=│α│ R)

Formula for calculating sector area of circular chain (circular arc system):

Sector area S= absolute value of central radian |a|× radius r/2

The absolute value of the circle center arc |a|= sector area S×2/ radius r

Arc length L= absolute value of central radian |a|× radius r

Sector area S= arc length L× radius r/2

Derivation of Sector Area Formula 2 There are two expressions of Sector Area Formula:

(1)S fan =(n/360)πR(n is the central angle and r is the sector radius).

(2)S fan = 1/2lr (when the arc length is known) l is the arc length and r is the sector radius.

Note: π is pi, which is about 3. 14 15926535, generally 3. 14.

Extended data:

Sector circumference formula, because the sector = two radii+arc length, if the radius is r and the central angle of the sector is n, then the sector circumference:

C=2R+nπR÷ 180 .

Department component:

1. The part between point A and point B on the circle is simply called "arc" and is pronounced as "arc AB" or "arc AB".

2. The angle with the center of the circle as the center point is called the "central angle".

3. A statistical chart is a "fan chart".

The formula of sector area is deduced as follows: sector perimeter = sector radius ×2+ arc length, that is, c = 2r+(n ÷ 360) π d = 2r+(n ÷180) π r. The formula of sector area is S=(lR)/2 or s = (180).

A figure surrounded by an arc and two radii passing through both ends of the arc is called a fan (the combination of a semicircle and a diameter is also a fan). The formula of sector perimeter is: sector perimeter = sector radius ×2+ arc length, that is, c = 2r+(n ÷ 360) π d = 2r+(n ÷180) π r sector area formula describes the relationship between sector area and central angle (vertex angle), radius and opposite arc length. The mathematical formula is: s fan =(lR)/2 (l is the arc length of the sector) =( 1/2)θR(θ is the central angle in radians).

A sector (symbol:) is a part of a circle surrounded by two radii and an arc. The smaller area is called a small sector, and the larger area is called a large sector. θ is the angular radian of the sector, r is the radius of the circle, and l is the arc length of the small sector. A sector with an arc of 180 is called a semicircle. Other circular arc angle sectors are sometimes given special names, including quadrant angle (90), sextant angle (60) and octupler angle (45), which are round 1/4, 1/6 and 1/8 respectively.