How do you find the area of a sector in geometry?

How do you find the area of a sector in geometry?

What is the Formula for Area of a Sector?

1. Area of a Sector of Circle = (θ/360º) × πr2, where, θ is the angle subtended at the center, given in degrees, r is the radius of the circle.
2. Area of a Sector of Circle = 1/2 × r2θ, where, θ is the angle subtended at the center, given in radians, r is the radius of the circle.

How do you solve a sector problem?

Sectors and Circles Problems

1. The formula for the arc length is given by. arc length AB = r * angle AOB.
2. arc length AB is given and is equal to 2r, hence. 2r = r * angle AOB.
3. Solve for angle AOB to obtain. angle AOB = 2 radians.
4. The area of the sector is given by. Area = (1/2) * angle AOB * r 2 = (1/2) * 2 * r 2 = r 2

What is Theorem 3.14 area of a sector?

Area of a sector when the central angle is given in degrees Pi (π) = 3.14 and r = the radius of a sector.

How do you find the arc length and area of a sector?

To calculate arc length without radius, you need the central angle and the sector area:

1. Multiply the area by 2 and divide the result by the central angle in radians.
2. Find the square root of this division.
3. Multiply this root by the central angle again to get the arc length.

What is a sector in geometry?

Sector. A sector is a region bounded by two radii of a circle and the intercepted arc of the circle. The angle formed by the two radii is called a central angle. A sector with a central angle less than 180° is called a minor sector.

How to calculate the area of a sector?

Solution to Problem 2: The formula for the area of a sector is. Area = (1 / 2) * angle of sector * r 2 The area and the angle are given. The angle is given in degrees and has to be converted into radians. Solve for radius r to obtain. r = square root [ 2 * 20 * 180 / (40 Pi) ] The arc length is given by. arc length of sector = angle of sector * r

How to calculate the arc length of a sector?

The angle of a sector in a given circle is 40 degrees and the area of the sector is equal to 20 cm 2. Calculate the arc length of the sector. Solution to Problem 2: The formula for the area of a sector is. Area = (1 / 2) * angle of sector * r 2. The area and the angle are given.

Which is the angle of a sector in a given circle?

The angle of a sector in a given circle is 40 degrees and the area of the sector is equal to 20 cm 2.