To calculate the surface area of the rectangular pyramid, we need to find the area of each face and add them together.
First, we can find the area of the rectangular base:
Area of base = length * width = 5 in * 4 in = 20 in^2
Next, we can find the area of the large triangular face:
Area of large face = 1/2 * base * height = 1/2 * 5 in * 6.8 in = 17 in^2
Similarly, we can find the area of the small triangular face:
Area of small face = 1/2 * base * height = 1/2 * 4 in * 7 in = 14 in^2
Finally, we need to find the area of the two remaining triangular faces. These two faces are congruent triangles with base equal to the slant height of the pyramid and height equal to the height of the rectangular face. We can use the Pythagorean theorem to find the slant height of the pyramid:
Slant height = sqrt((base/2)^2 + height^2) = sqrt((2.5 in)^2 + (6.8 in)^2) ≈ 7.25 in
Then, we can find the area of each triangular face:
Area of triangular face = 1/2 * base * height = 1/2 * 7.25 in * 6.8 inArea of triangular face ≈ 24.65 in^2
Now we can add up the areas of all the faces to find the total surface area of the pyramid:
Total surface area = Area of base + Area of large face + Area of small face + 2 * Area of triangular face
Total surface area = 20 in^2 + 17 in^2 + 14 in^2 + 2 * 24.65 in^2
Total surface area ≈ 100.3 in^2
Therefore, approximately 100.3 square inches of wrapping paper would be needed to cover the pyramid without overlapping.
Rounding this value to the nearest whole number, we get 100 in^2 as the answer option that is closest to the calculated value. Therefore, the answer is 102 in^2.