The least amount of cardboard needed to make the box is 358 square inches.
To determine the least amount of cardboard needed to make a box that measures 7 inches by 12 inches by 5 inches, we need to calculate the surface area of the box. This can be done by finding the areas of each of the six sides of the box and adding them together.
The dimensions of the box are:
Length (L) = 12 inches
Width (W) = 7 inches
Height (H) = 5 inches
The area of each side can be calculated using the formula:
Area = L × W
Here's a breakdown of the areas for each side:
Top and bottom sides: 12 inches × 7 inches = 84 square inches
Front and back sides: 12 inches × 5 inches = 60 square inches
Left and right sides: 7 inches × 5 inches = 35 square inches
Now, we add up the areas of all six sides to find the total surface area:
Total surface area = 2 × (84 square inches + 60 square inches + 35 square inches)
Total surface area = 2 × 179 square inches
Total surface area = 358 square inches
Therefore, the least amount of cardboard needed to make the box is 358 square inches.