To find the area of a segment in a circle, you need to know two main things: the radius of the circle and the angle of the segment. The angle can be measured in degrees or radians.
Here’s a simple guide to help you step-by-step:
Find the Area of the Sector:
First, calculate the area of the sector. Use this formula if you have the angle in degrees:
[
\text{Area of Sector} = \frac{\theta}{360} \times \pi r^2
]
If the angle is in radians, use this formula instead:
[
\text{Area of Sector} = \frac{r^2 \theta}{2}
]
Calculate the Area of the Triangle:
Next, find the area of the triangle that is formed by the two radii and the line connecting them. Use this formula:
[
\text{Area of Triangle} = \frac{1}{2} r^2 \sin(\theta)
]
Find the Area of the Segment:
Finally, to find the area of the segment, subtract the area of the triangle from the area of the sector:
[
\text{Area of Segment} = \text{Area of Sector} - \text{Area of Triangle}
]
And that’s it! Just plug in your numbers, and you’ll have the area of the segment in no time.
To find the area of a segment in a circle, you need to know two main things: the radius of the circle and the angle of the segment. The angle can be measured in degrees or radians.
Here’s a simple guide to help you step-by-step:
Find the Area of the Sector:
First, calculate the area of the sector. Use this formula if you have the angle in degrees:
[
\text{Area of Sector} = \frac{\theta}{360} \times \pi r^2
]
If the angle is in radians, use this formula instead:
[
\text{Area of Sector} = \frac{r^2 \theta}{2}
]
Calculate the Area of the Triangle:
Next, find the area of the triangle that is formed by the two radii and the line connecting them. Use this formula:
[
\text{Area of Triangle} = \frac{1}{2} r^2 \sin(\theta)
]
Find the Area of the Segment:
Finally, to find the area of the segment, subtract the area of the triangle from the area of the sector:
[
\text{Area of Segment} = \text{Area of Sector} - \text{Area of Triangle}
]
And that’s it! Just plug in your numbers, and you’ll have the area of the segment in no time.