What is the area of a sector of a circle with a radius of 12 cm and a central angle of 130 degrees in terms of π?

To find the area of a sector of a circle, you can use the formula:

[

\text{Area} = \frac{\theta}{360} \times \pi r^2

]

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

In this case, the radius ( r ) is 12 cm, and the central angle ( \theta ) is 130 degrees.

First, calculate the area of the entire circle:

[

\text{Area of the circle} = \pi r^2 = \pi \times (12)^2 = 144\pi \text{ cm}^2.

]

Next, substitute these values into the sector area formula:

[

\text{Area of the sector} = \frac{130}{360} \times 144\pi.

]

Now, simplify ( \frac{130}{360} ):

[

\frac{130}{360} = \frac{13}{36}.

]

Then, substitute this back into the equation:

[

\text{Area of the sector} = \frac{13}{36} \times 144\pi