Mathematics for the first year of high school Finding the Perimeter and Area of a Fan .

The radius does not need to be converted into m, it is directly calculated in radius units.

1° = 180 rad (conversion of radians and angles) The length of the arc: l=a*r, where a is the unit radian of the central angle corresponding to the length of the arc or the length of the arc: l=a* *r 180 where a is the unit of the central angle corresponding to the length of the arc °

Fan area: The area enclosed by the two radii and the arc length corresponding to the angle between the two radii Fan perimeter: C fan = 2r + L

Therefore: sfan=l*r 2 (radian fan area formula) a* *r 2) 360 (angle fan area formula) r=15 cm, a=54°

l=a*π*r/180=54* (cm)

Sfan=A* *R2) 360=54* (cm2)C=2R+L=2*15+ (cm).

r=15 cm, a=54°=54°*π/180 = (rad)l=a*r= (cm)

Sfan = l*r 2= (cm2).

C fan = 2r + l = 2 * 15+ (cm).

The results are the same for both algorithms.

You can think of it as the ratio of a part of a circle to a whole circle as the ratio of angle to 2.

So the circumference of the sector is 2r+ the length of the arc.

The length of the arc can be solved using the following method.

Arc: circumference = angle: 2 (the angle should be represented by , 1° = 180) The area is similar. Sector area: area of a circle = angle: 2

Sum up. c = 2r + angle * * r 180

s = angle * r 2 * 360

1. Multiply the area of the circle by 54/360 to find the sector area!

2. Similarly, multiply the circumference of the circle by 54/360 to find the fan-shaped circumference!

It is the radian system, and the unit of radius is the meter, which is calculated according to the standard unit.

The formula for the perimeter of the sector is: the perimeter of the sector = the radius of the sector 2 + the arc length, that is, c=2r+ (n 360) d=2r+(n 180) r. Sector area formulais s=(lr) 2 or s=(1 2) r.

r is the radius of the base circle, and l is the length of the sector arc.

is the central angle of the circle. The area of the sector = the area of the circle * the degree of the central angle of the circle 360°;

The circumference of the fan = the straight lifting diameter + the perimeter of the fan * the degree of the angle of the car in the center of the circle 360°.

Introduction to the fanThe shape enclosed 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). Obviously, it is made up of a part of the circumference of the circle and its corresponding central angle. "Duan Yinxian Geometric Original".

defines a sector as a figure enclosed by vertices on either side of the corner at the center of the circle and a section of an arc truncated on both sides.

Full formula for fan:

1. The area formula of the fan: s=lr 2 (r is the radius of the fan, and l is the arc length corresponding to the fan.)

2. The arc length of the fan = 2 r angle 360

3. Sector circumference = radius 2 + arc length c=2r+(n 360) d=2r+(n 180) r

The shape enclosed 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). Obviously, it is made up of a part of the circumference of the circle and its corresponding central angle. The definition of the fan in the Geometry is as follows:

A figure enclosed by two sides of the corner where the vertex is at the center of the circle and a section of the arc that is truncated on both sides.

Scalloped circumference. If the radius is R and the diameter is d, the degree of the central angle of the circle to which the fan excites is n°.

c=2r+（n÷360）πd=2r+（n÷180）πr

The degree of the central angle of the circle opposite by the sector is n°, the radius of the major circle is r, and the radius of the minor circle is r.

c=2*（r-r）+πr+r）/180*n

If the two circles are not concentric, the angles are n, m, respectively. The radius of the great circle is r, and the radius of the minor circle is r.

c=2*（r-r）+πr*n+r*m）/180

The fan-shaped Beixiang arc is long.

The length of an arc that passes 2 points on a circle is called arc length. n is the number of angles at the center of the circle, and r is the radius, which is the radian of the angle at the center of the circle.

l=nπr÷180

l=n/180·πr

l=|αrl=n°πr÷180°

1. Formula for calculating the arc length of the fan:

Arc length = number of angles at the center of the circle 360° 2 pi radius;

l is the arc length, n is the central angle of the fan, is the pi, and r is the radius of the fan.

2. Area formula:

r is the radius of the fan, n is the number of angles of the arc to the center of the circle, is the pi, and l is the arc length corresponding to the fan.

It is also possible to divide the area of the circle where the fan-shaped ballast is located by 360 and multiply by the angle n of the central angle of the fan-shaped circle, as follows:

Sector area s = angle of the central angle (angle system) pi radius r 360°.

Composition of the Ogi guess shape:

A fan (symbol: ) is a part of a circle enclosed by two radii and a segment of arcs, and is called a small sector in a smaller area and a large sector in a larger area. In Figure 1 on the right, 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 fan-shaped arc angles sometimes give them special royal names, including quadrant angles (90°), sixths (60°), and eighths (45°), which are full circle 8s, respectively.

How to find the formula for calculating the perimeter and area of a fan?

Sector Perimeter = Arc Length + 2 * Radius.

Arc length = (central angle 360) * circumference.

Therefore, the radius can be calculated by the perimeter.

Then use the radius to find the area of the fan:

Sector area = (center angle 360) * circle area.

The perimeter of the sector = two radii + arc length (arc length = n r 180).

Area of the sector = n r 360 = 1 2 arc length radius.

where (n denotes the central angle and r denotes the radius).

The radius r of the circle is obtained by using the area of the circle, connecting the center of the circle, the vertex of the sector and the tangent point into a right triangle, and the hypotenuse c is obtained by using the straight side r and the diagonal 1 2, and the radius of the sector is r=c+r.

Use the radius r and degrees to get the sector area and perimeter.

The hypotenuse extends to the tangent point, which is the fan radius.

Sector circumference: c=n r 180 or c=lr 2

Sector area: s=n n r 360

How to find the formula for calculating the perimeter and area of a fan?

Sector Perimeter = Arc Length + 2 * Radius.

Arc length = (central angle 360) * circumference.

Therefore, the radius can be calculated by the perimeter.

Then use the radius to find the area of the fan:

Sector area = (center angle 360) * circle area.

s maximum; ∵c＝2r+l.

Sector area s=; 2, so when a l , the arc length is l; c Solution; 2;4 o'clock; 4) = 2; 2), at this time l c-2r c-2 (c5cr(r<,s maximum, by the property of the quadratic function; [2*(-1))=c/.5c/,l＝c-2r>4)=c/c/(c/.

s=0, r<, then a l :

Let the radius be r; 2) r=(c, when r -0; r