Question 958126
surface area is the sum of the areas of each face.


if you double the dimensions, you quadruple the area.


if the surface area is 350 mm^2, and the scale factor is 2, then the surface area will be quadrupled to 1400 mm^2.


for example:


let a rectangular prism have a length of L and a width of W and a height of H.


The surface area of the prism will be:


(2 * L * W) + (2 * L * H) plus (2 * W * H).


if the scale factor is 2, then each dimension is multiplied by a factor of 2.


the surface area of the scaled prism will then be:


(2 * 2 * L * 2 * W) + (2 * 2 * L + 2 * H) plus (2 * 2 * W * 2 * H).


simplify that equation and you get:


the surface area of the scaled prism will be:


(8 * L * W) + (8 * L * H) + (8 * W * H).


The surface area went from 2 * the area of each face to 8 * the area of each face.


That's a scale factor of 8 / 2 = 4.


4 is equal to 2^2.


The scale factor of the surface area is equal to the square of the scale factor of the dimensions.