Question

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

Answer 1

Answer:

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