Final answer:
To find the area of the shaded sector, divide the arc length of the sector by the circumference of the circle and multiply it by the area of the entire circle. Round the final answer to the nearest hundredth.
Step-by-step explanation:
To find the area of the shaded sector, we need to calculate the fraction of the circle that is shaded and multiply it by the area of the entire circle. First, find the angle of the shaded sector by dividing the arc length of the sector by the length of the entire circumference and multiply it by 360 degrees. Next, calculate the area of the entire circle using the formula A = πr^2, where r is the radius of the circle. Finally, multiply the fraction of the circle that is shaded by the area of the entire circle to find the area of the shaded sector. Round your answer to the nearest hundredth.