Question

What is the measure of arc ADB? What is the length of arc ADB? What is the area of the shaded region?

Answer 1

What is the measure of arc ADB?
 The measure of the arc for this case is given by the following angle:
 theta = 360-90
 theta = 270 degrees

 What is the length of arc ADB? 

 The arc length is given by:
 s = R * theta
 Substituting values:
 s = 15 * (270 * (pi / 180))
 s = 70.69 m

 What is the area of the shaded region?

 The area of the shaded region is:
 A = (s' / s) * (pi) * (r ^ 2)
 Substituting values:
 A = (270/360) * (3.14) * (15 ^ 2)
 A = 529,875 m ^ 2