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