To find the area of a circular sector (which is like a slice of pizza), you can use this easy formula:

$A = \frac{1}{2} r^2 \theta$

Here's what the letters mean:

• ( A ) is the area of the sector.
• ( r ) is the radius of the circle (the distance from the center to the edge).
• ( \theta ) is the central angle measured in radians.

Changing Degrees to Radians

If you have the angle ( \theta ) in degrees, you can change it to radians using this formula:

$\theta \, \text{(radians)} = \frac{\theta \, \text{(degrees)} \times \pi}{180}$

Example Calculation

Let's say we have a circle with a radius of ( r = 4 ) units and a central angle of ( \theta = 60^\circ ).

1. First, we need to change ( 60^\circ ) to radians: $60 \times \frac{\pi}{180} = \frac{\pi}{3}$

2. Now we can calculate the area: $A = \frac{1}{2} \times 4^2 \times \frac{\pi}{3}$

   This simplifies to: $A = \frac{8\pi}{3} \text{ square units}$

And that's it! Now you know how to find the area of a circular sector!