A square pyramid has a height of 25 ft and each side of the base has a length of 15 ft.

If a model of the square pyramid is scaled down by a factor of, what is the surface area of the model?

Surface area of square pyramid is computed as follows:

A = a² + a*√ (a² + 4h²)

where a is the base length and h is the height.

If a model of the square pyramid is scaled down by a factor of x, then the surface area will be:

A' = (a/x) ² + (a/x) * √[ (a/x) ² + 4 (h/x) ²]

A' = a²/x² + a/x * √[a²/x² + 4h²/x²]

A' = a²/x² + a/x * √[ (a² + 4h²) / x²]

A' = a²/x² + a/x * √ (a² + 4h²) / √x²

A' = a²/x² + a/x² * √ (a² + 4h²)

A' = 1/x² * [a² + a*√ (a² + 4h²) ]

A' = 1/x² * A

That is, the surface area will be 1/x² times the original surface area. If h = 25 ft and a = 15 ft:

A = 15² + 15*√ (15² + 4 (25) ²) = 1008.02 ft²

The factor is not mentioned in the question, nevertheless, the area will be 1008.02/factor² ft²