How to Find the Area of a Segment of a Circle

To find the area of a segment of a circle, you can follow these steps:

1. Understand the components: A segment of a circle is the area between a chord and the arc that connects the endpoints of the chord. You’ll need to know the radius of the circle and the angle (in radians) subtended by the chord at the center of the circle.
2. Calculate the area of the sector: The area of the sector (the pie-slice shape) can be found using the formula: Area of Sector = (θ/2) * r², where θ is the angle in radians and r is the radius.
3. Calculate the area of the triangle: To find the area of the triangle formed by the center of the circle and the endpoints of the chord, use the formula: Area of Triangle = (1/2) * r * r * sin(θ).
4. Subtract the area of the triangle from the area of the sector: Finally, the area of the segment can be found by subtracting the area of the triangle from the area of the sector. So, use the formula: Area of Segment = Area of Sector - Area of Triangle.

In summary, the formula to find the area of a segment of a circle is:

Area of Segment = (θ/2) * r² - (1/2) * r * r * sin(θ)

Make sure the angle is in radians when performing your calculations, as this will ensure accuracy in your results.