The sides of the base of a right Square pyramid are 3 Meters in length, And it's slant height is 6 m. If the length of the side of the base and the slant height are each multiplied by 3, by what factor is the surface area X?

9

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 3, p is the perimeter that is the sum of the sides, and since there are 4 sides, then it would be 12 (3 * 4), h the inclined height is 6, replacing we are left with:

As = 1/2 * 12 * 6 + 3 ^ 2

Ace = 45

Now they say the sides and the tilt height are multiplied by 3, the sides now measure 9, therefore the perimeter is 36 (4 * 9), the height would be 18, the replacement would be:

Ace = 1/2 * 36 * 18 + 9 ^ 2

Ace = 405

Therefore, the factor would be:

405/45 = 9

Which means that the factor is 9.