Formula: Area of a segment of a circle simple definition
The area of a segment of a circle is the region enclosed between a chord and the corresponding arc of a circle.
The formula for the area of a segment of a circle is calculated using the central angle of the segment and the radius of the circle. The area can be found by first finding the area of the corresponding sector (a portion of the whole circle) and then subtracting the area of the corresponding triangle.
Here are the steps to calculate the area of a segment of a circle:
1. Determine the central angle of the segment, which is the angle between the two radii that form the boundaries of the segment.
2. Use the formula for the area of a sector: Area of sector = (central angle / 360°) * π * r^2, where r is the radius of the circle.
3. Calculate the area of the corresponding triangle: Area of triangle = (1/2) * base * height, where the base is equal to the length of the chord (the line segment connecting the endpoints of the segment) and the height is the distance from the midpoint of the base to the center of the circle.
4. Subtract the area of the triangle from the area of the sector to get the final area of the segment.
Note that the formula assumes the circle is a perfect circle and all measurements are in the same units (e.g., inches, centimeters).
The area of a segment of a circle is the region enclosed by a chord of the circle and the arc of the circle intercepted by the chord. To find the area of a segment, you can use the following formula:
Area of segment = (θ/360) x πr^2 - (1/2) x r^2 x sin(θ)
Here's how to use the formula to find the area of a segment:
1. Determine the central angle (θ) of the segment in degrees.
2. Measure the radius (r) of the circle.
3. Plug the values of θ and r into the formula.
4. Calculate the values inside the formula.
5. Simplify and evaluate the expression.
6. The result will be the area of the segment.
It is important to note that the angle (θ) must be given in degrees, and the trigonometric function sin(θ) should be calculated using the angle measured in radians.