You can think of this as the area of a rectangle and half of a circle.
The radius of a circle is 6 feet. This means that the diameter is 12 feet. The diameter is also the width of the rectangle.
The area of the rectangle is (19 feet)(12 feet) = 228 square feet.
The area of the circle is (6 feet)2π = 36?, or approximately 113 square feet.
We already counted half of the circle though, so we only need half of the area.
If the area of the whole circle is approximately 113 square feet, then the area of half of the circle is approximately 56.5 square feet.
Now we just need to add the two together: 228 square feet + 56.5 square feet ≈ 284.5 square feet