What is the formula for the area of a sector of a circle?

To calculate the area of a sector of a circle we have to multiply the central angle by the radius squared, and divide it by 2. Area of a sector of a circle = (θ × r2 )/2 where θ is measured in radians. The formula can also be represented as Sector Area = (θ/360°) × πr2, where θ is measured in degrees.

What is the formula for arc area?

The formula for sector area is simple – multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2.

What is the formula for finding the area of a sector of a circle with radius R?

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

How do you find the arc length and area?

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.

How do you find the area of a circle with an arc?

Find the area of the circle by squaring the radius and multiplying that by 3.14 (pi). For example, if the radius is 10 cm, square 10 to get 100. Then multiply 100 times 3.14 to get a circle area of 314 square cm. Multiply your answer from Step 1 by your answer from Step 2 to find the area of the arc’s sector.

What is the area of a sector?

The area of a sector is the region enclosed by the two radii of a circle and the arc. In simple words, the area of a sector is a fraction of the area of the circle.

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

Which explanation justifies how the area of a sector of a circle is derived?

The answer is in fractional form and also uses π as this is an exact value.