Final answer:
The modified surface area of a square pyramid, with the side length tripled and slant height divided by 5, is calculated as 9s^2 + 6sl/5, where 's' is the original side length and 'l' is the original slant height.
Step-by-step explanation:
To find the modified surface area of the square pyramid when the side length is tripled and the slant height is divided by 5, we need to recall the formula for the surface area of a square pyramid. The original surface area formula for a square pyramid is given by the sum of the area of the base plus the area of the four triangular faces, which can be represented as:
Surface Area = base area + 4 × (1/2 × slant height × side length)
For the modified pyramid, if the original side length is 's' and the slant height is 'l', tripling the side length would make it '3s' and dividing the slant height by 5 would make it 'l/5'. Using these new values, the formula for the modified surface area becomes:
Modified Surface Area = (3s)^2 + 4 × (1/2 × (l/5) × 3s)
Simplifying, we get:
Modified Surface Area = 9s^2 + 6s(l/5)
This accounts for the nine-fold increase in the base area (since area is proportional to the side length squared) and the change in the area of the triangular faces.