Final answer:
The area of the sector with a radius of 4 and a central angle of 270 degrees is 12π square units, which is approximately 37.6991 square units.
Step-by-step explanation:
The area of a sector of a circle can be found using the formula:
A = (θ/360) × πr²
This formula uses the central angle θ, in degrees, and the radius r of the circle. Since the given central angle is 270 degrees and the radius is 4, we can calculate the area of the sector accordingly. Plugging the given values into the formula will give us:
A = (270/360) × π×4²
Reducing 270/360 to 3/4 and calculating π times the square of the radius (16), we get:
A = 3/4 × π × 16
So the area of the sector is:
A = 12π square units
This is approximately 37.6991 square units when π is approximated as 3.14159.