1. **State the problem:** We have a rectangular prism box with a base measuring 4 feet by 5 feet and a total surface area of 148 square feet. We need to find the height of the box. 2. **Formula for surface area of a rectangular prism:** $$SA = 2lw + 2lh + 2wh$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Identify known values:** - Length $l = 5$ ft - Width $w = 4$ ft - Surface area $SA = 148$ sq ft 4. **Substitute known values into the formula:** $$148 = 2(5)(4) + 2(5)h + 2(4)h$$ 5. **Simplify the constants:** $$148 = 40 + 10h + 8h$$ 6. **Combine like terms:** $$148 = 40 + 18h$$ 7. **Isolate the term with $h$ by subtracting 40 from both sides:** $$148 - 40 = 18h$$ $$108 = 18h$$ 8. **Divide both sides by 18 to solve for $h$:** $$\frac{108}{\cancel{18}} = \frac{18h}{\cancel{18}}$$ $$6 = h$$ 9. **Final answer:** The height of the box is **6 feet**.