The rectangular prisma has 6 faces. The area of the front and back faces is
The area of the base faces is
and the area of the lateral faces is
Then, the total surface area is the sum of the above results, that is,
By combining similar terms, it gives
Now, from the given information, we know that the surface area must be equal to 298 square feet. So, we have
Then, by subtracting 56 to both sides, we have
and by dividing both sides by 22, we get
Therefore, the answer is 11 feet