Final answer:
Ryan will need 148 cm² of wrapping paper to cover a rectangular box with dimensions of 11 cm by 2 cm by 4 cm, as this is the total surface area of the box.
Step-by-step explanation:
To determine the amount of wrapping paper needed for a rectangular box, we calculate the surface area of the box. For a box with dimensions 11 cm by 2 cm by 4 cm, we find the surface area by calculating the areas of all six sides.
The area of the two side faces is 2 x (11 cm x 2 cm) = 44 cm².
The area of the front and back faces is 2 x (11 cm x 4 cm) = 88 cm².
The area of the top and bottom faces is 2 x (2 cm x 4 cm) = 16 cm².
Add these areas together to find the total surface area:
44 cm² + 88 cm² + 16 cm² = 148 cm²
Therefore, Ryan will need 148 cm² of wrapping paper to cover the rectangular box.