Example 1:Find the area of the shaded region. Example 2:Find the radius of the circle if the area of the shaded region is 50π Show Video Lesson Formula For Area Of Sector (In Radians) Next, we will look at the formula for the area of a sector where the central angle is measured ...
To calculate the area of a sector, a simple formula can be used. Sector Area Formula Theareaof a sector can be found using the formula: sector area =1/2r²θ Thus, a sector’s area is equal to the radiusrsquared times the central angleθin radians, divided by 2. If you know th...
Area of Sector in Radians If we need to find the area of sector when the angle is given in radians, we use the formula, Area of sector = (1/2) × r2θ; where θ is the angle subtended at the center, given in radians, and 'r' is the radius of the circle. So, let us unders...
Therefore, α must be given in radians. A is the area we want to determine, so we solve for A again: A=πr2α2π=r2α2 The above expression is also an area of a sector formula, but this time the central angle is measured in radians. Example 1: Area of a Sector of a Circle ...
To find the central angle of a sector of a circle, you can invert the formula for its area: A = r² ·α/2, where: r— The radius; and α— The central angle in radians. The formula for α is then: α = 2 · A/r² To find the angle in degrees, multiply the result by...
Learn how to find the arc length of a sector with the formula and examples. Understand the formula and the method to find the area of a sector with...
‘θ’here refers to the angle in radians. Now let us incorporate the value ofθin the area of the sector: Area of Sector = A = (θ) ×πr2 A = (L/r) × (r2/2) A = (L × r)/2 Perimeter Formula for a Sector As we know that perimeter refers to the summation of the le...
Area of SegmentThe Area of a Segment is the area of a sector minus the triangular piece shaded blue below:There is a lengthy reason, but the result is a slight modification of the Sector formula:Area of Segment = θ − sin(θ)2× r2 (when θ is in radians)...
Area of a Sector Formula The area of a sector of a circle where the central angle is indegreesis:A=θ360πr2 The area of a sector of a circle where the central angle is inradiansis:A=θ2r2 where θ is the central angle and r is the radius of the circle. ...
In summary, the formula to find the area of a sector in a circle is A = (πr^2θ)/360, where θ is the central angle in degrees. If θ is in radians, the formula becomes A = (r^2θ)/2. The sector area is simply a fraction of the total area of the circle. ...