The height of an equilateral triangular prism increases by one unit. The new lateral area is more than the original by how much?

Question

Answer

the perimeter of the base

the area of the base

the height

the area of one lateral face

Answer 1

I will assume that by "lateral area" you mean the surface area without the two triangular bases

So if the side of the equilateral triangle is s and the height is h, then the area of the three rectangles is 3sh
new height is (h+1)
so new area = 3s(h+1)
= 3sh + 3s
so the increase is 3s, which is the "perimeter of the base"