Final answer:
Sage needs 260 square inches of gift wrap to cover the shoe box with enough overlap. This is calculated by determining the shoe box's total surface area and then adding an additional 20% for overlap.
Step-by-step explanation:
The student seeks to find the amount of gift wrap needed to cover the shoe box and provide for overlap. To calculate this, we first need to determine the surface area of the box and then increase it by 20% as stated. First, we calculate the surface area of the box: we have two ends that are 10 inches by 3 inches, two sides that are 6 inches by 3 inches, and the top and bottom which are 10 inches by 6 inches each. Therefore, the total surface area (SA) can be found by the formula:
SA = 2(lw + lh + wh)
SA = 2(10*6 + 10*3 + 6*3)
SA = 2(60 + 30 + 18)
SA = 2(108)
SA = 216 inches²
Now, we need 20% more than the total surface area for overlap:
Additional wrap needed = SA * 20%
Additional wrap needed = 216 * 0.2
Additional wrap needed = 43.2 inches²
So, the total gift wrap needed is:
Total wrap = SA + Additional wrap
Total wrap = 216 + 43.2
Total wrap = 259.2 inches²
To ensure Sage has enough wrap, she should round up to the nearest whole number of square inches. Therefore, Sage needs 260 square inches of gift wrap.