Final answer:
To determine the radian and degree measures of the central angle subtended by the arc, divide the length of the arc by the radius of the circle. Then, convert the radian measure to degrees. To find the area of the sector, use the formula A = (1/2)r²Δθ.
Step-by-step explanation:
To determine the radian measure of the central angle subtended by the arc, we can use the formula Δθ = s/r, where s is the length of the arc and r is the radius of the circle. Substituting the values, we get Δθ = 11/5. To convert this to degrees, we can use the fact that there are 2π radians in 360 degrees. So, the degree measure of the central angle is Δθ * (180/π).
Now, let's calculate the area of the sector. The area of a sector can be found using the formula A = (1/2)r²Δθ. Substituting the values, we get A = (1/2) * 5² * (Δθ).