Question

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

A)the area of the base

B)the height

C)the perimeter of the base

D)the area of one lateral face

Answer 1

The surface area increased by the amount of area of the 3 rectangles on the upper part of each side. The width of each rectangle is 1 unit. The length of each rectangle is a.
The total increase in area is 1a + 1a + 1a = 3a
Since the base of the prism is an equilateral triangle with side a, the perimeter of the base is a + a + a = 3a.
The increase in lateral area, 3a = the perimeter, 3a

Answer 2

thank you!

Answer 3

you're welcome