A circle has a radius of 6 centimeters.What is the area of the sector formed by a central angle measuring 2.4 radians?Enter your answer as a decimal.

- A central angle is basically an angle that is located at the center of the circle and is created where two radii (plural of radius) join (example of a central angle in dark blue in the picture).
- A sector is created from the area sectioned off by the central angle (light blue in picture).
- Imagine a pizza - the sector is a pizza slice and the central angle is the angle of the pointy end of the pizza.

To calculate the area of the sector, you find what fraction of the angle of the full circle is part of the central angle and multiply that fraction by the area of the circle: 
[tex]A = \frac{\theta}{2 \pi } \pi r^{2} [/tex]
where A = area of sector, θ = measurement of central angle, [tex] \pi r^{2} [/tex] = equation for area of circle

Since our units are in radians instead of degrees, 2π is the angle of the full circle and θ = 2.4 rad. We also know the radius of the circle, r = 6 cm. Now plug these values into the equation for the area of a sector:
[tex]A = \frac{\theta}{2 \pi } \pi r^{2}\\ A = \frac{2.4}{2 \pi } \pi (6)^{2}\\ A = \frac{2.4}{2 \pi } \pi (6)^{2} A = 43.2 cm^{2} [/tex]

Your answer is 43.2 [tex]cm^{2} [/tex].