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Area of a Sector of a Circle is basically, a sector is the portion of a circle. To Know more on circle, sector of a circle and for more solved examples and solution visit Byju's.
- Area Of a Sector Formula
So if a sector of any circle of radius r measures θ, area of...
- Area Of a Sector Formula
Area of a Sector of Circle = 1/2 × r 2 θ, where, θ is the sector angle subtended by the arc at the center, in radians, and 'r' is the radius of the circle. Area of Sector Formula Derivation. Let us apply the unitary method to derive the formula for the area of the sector of a circle. We know that a complete circle measures 360º.
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 × r 2 )/2 where θ is measured in radians.
So if a sector of any circle of radius r measures θ, area of the sector can be given by: Area of sector = \(\begin{array}{l}\frac{\theta }{360} \times \pi r^{2}\end{array} \)
The area of a sector is the area of the region enclosed by an arc and two radii of a circle. It represents a part of the area of a circle. Area of a sector is measured in square units, depending on the unit of the radius.
To calculate the area of a sector, we use the formula for the area of the circle as the basis. The only difference is that instead of figuring out the area of a complete circle, we are figuring out the area of a portion or part of that circle.
In geometry you learned that the area of a circle of radius \(r \) is \(\pi r^2 \). We will now learn how to find the area of a sector of a circle. A sector is the region bounded by a central angle and its intercepted arc, such as the shaded region in Figure 4.3.1.
