Final answer:
The total surface area of a covered box that is 4 inches long, 3 inches wide, and 6 inches high is 108 in.².
Step-by-step explanation:
To find the total area of a covered box, we need to calculate the surface area, which includes all six faces of the box. We have three pairs of opposite faces: two with dimensions 4 inches by 3 inches, two with dimensions 4 inches by 6 inches, and two with dimensions 3 inches by 6 inches.
To calculate the total area for each pair, we will use the formula area = length × width for rectangles.
Thus, for the first pair (4in × 3in), the total area is 2 × (4in × 3in) = 24 in.².
For the second pair (4in × 6in), it's 2 × (4in × 6in) = 48 in.².
And for the third pair (3in × 6in), it's 2 × (3in × 6in) = 36 in.².
Adding the areas together, we get the total surface area as 24 in.² + 48 in.² + 36 in.² = 108 in.².