The sides of the base of a right square pyramid are 3 meters in length, and its slant height is 6 meters. If the lengths of the sides of the base and the slant height are each multiplied by 3, by what factor is the surface area multiplied?

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.

Hopes This Helps :)

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.