How can you find the area of a segment of a circle?

To find the area of a segment of a circle, you first calculate the area of the sector that the segment is part of. A sector is the 'pie-slice' shape created by two radii and the arc between them. The formula to find the area of a sector is given by:

[ \text{Area of the sector} = \frac{\theta}{360} \times \pi r^2 ]

where ( \theta ) is the angle of the sector in degrees, and ( r ) is the radius of the circle.

Once you have the area of the sector, the next step is to find the area of the triangle formed by the two radii and the chord that closes the segment. The formula for the area of this triangle can be derived from trigonometry, using the sine of the angle, or it can be calculated using base and height based on the known radius and angle.

To determine the area of the segment, you subtract the area of the triangle from the area of the sector:

[ \text{Area of the segment} = \text{Area of the sector} - \text{Area of the triangle} ]

This method accurately gives you the area of the