The sides of the base of a right square pyramid are 4 m in length, and its slant height is 8 m. If the lengths of the sides of the base and the slant height are each multiplied by 4, by what factor is the surface area multiplied?

16

Step-by-step explanation:

We have that the total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base, therefore it would be equal to:

As = 1/2 * p * h + l ^ 2

where l are the sides that measure 4, p is the perimeter that is the sum of the sides, and since there are 4 sides then it would be 16 (4 * 4), h the inclined height is 8, replacing we are left with:

As = 1/2 * 16 * 8 + 4 ^ 2

Ace = 80

Now, they say that the sides and the tilt height are multiplied by 4, the sides now measures 16, therefore the perimeter is 64 (4 * 16), the height would be 32, replacing would be:

As = 1/2 * 64 * 32 + 16 ^ 2

As = 1280

Therefore the factor would be:

1280/80 = 16

This means that to calculate the new surface area, it must be multiplied by the square of the number by which the sides and the inclined height are multiplied, that is, 4 ^ 2 = 16.