Answer:
Surface area of square pyramid is computed as follows:
A = a² + a*√(a² + 4h²)
where <em>a</em> is the base length and <em>h</em> 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
