To find the area of the court that is painted blue, we need to find the area of the rectangle and the area of the half circle and then add them together.
The area of the rectangle is found by multiplying its length by its width: 15 feet * 16 feet = 240 square feet.
The area of the half circle is found by using the formula for the area of a circle: 0.5 * π * r^2. Since the diameter is given as 16 feet, the radius is half of that, which is 8 feet. Plugging in the values, we get: 0.5 * 3.14 * 8^2 = 0.5 * 3.14 * 64 = 100.48 square feet.
Now we add the two areas together to find the total area painted blue: 240 square feet + 100.48 square feet = 340.48 square feet.
Therefore, the correct answer is 340.48 ft2.