How do you find the shaded area of a sector?

How do you find the shaded area of a sector?

To find the area of the shaded segment, we need to subtract the area of the triangle from the area of the sector.

What is the formula for 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 area of a shaded region?

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons.

How do you find the measure of the central angle of the sector in degrees?

Find the central angle of a sector whose radius is 56 cm and the area is 144 cm2. 144 = (θ/360) x 3.14 x 56 x 56. Divide both sides by θ. Thus, the central angle is 5.26 degrees.

How do you find the arc length 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.

How do you find the measure of an arc?

A circle is 360° all the way around; therefore, if you divide an arc’s degree measure by 360°, you find the fraction of the circle’s circumference that the arc makes up. Then, if you multiply the length all the way around the circle (the circle’s circumference) by that fraction, you get the length along the arc.

How do you find the length of an arc of a sector?

Multiply the sector area by 2 and further, divide the result by the central angle in radians. Find the square root of the result of the division. Multiply this obtained root by the central angle again to get the arc length. The units of this calculated arc length will be the square root of the sector area units.

What is the shaded area of a circle called?

An arc is part of the circumference of a circle. If the arc is over half of the circumference then it is called a major arc. A sector is the area enclosed by 2 radii (radius) and an arc (It looks like a slice of cake or pizza).

How is the area of a shaded sector determined?

The area of the shaded sector can be determined using the formula StartFraction measure of angle Z Y X Over 360 degrees EndFraction (pi r squared). Which best explains the formula? The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

How do you calculate the sector area of a circle?

The formula for sector area is simple – multiply the central angle by the radius squared, and divide by 2: But where does it come from? You can find it by using proportions, all you need to remember is circle area formula (and we bet you do!): The area of a circle is calculated as A = πr².

What should be the angle of a sector?

You need to measure or know to things: the sector’s radius and its angle. If the sector is a quadrant, then the angle is 90°. There are different tools for measuring angles, depending on your particular situation.

What is the definition of a sector in geometry?

Sector definition So let’s start with the sector definition – what is a sector in geometry? A sector is a geometric figure bounded by two radii and the included arc of a circle