Question

What is the surface area of the prism? Include steps.

Answer 1

First things first. This is a rectangular prism, so it's faces are all rectangles.

Area of a rectangle: Area = Length x Height

- Rectangular Prism Dimensions:

Length: 3m
Width: 4m
Height: 2m


To calculate the surface area of a rectangular prism we first need to realize that he has 3 pairs of equal rectangles.

- The first pair (Photo 1):

Two rectangles with the same measure, so we can say that the area of this pair is: (L x H) x (L x H) or 2 x (L x H).

-> Area (Pair 1) = 2 x (3 x 2) = 2 x 6 = 12m^2

But if we will do the same thing to 3 different pairs, we can describe that:

- Total Surface Area (At):

At = 2 x (L x H) + 2 x (L x H) + 2 x (L x H)

-> At = 2 x ((L x H) + (L x H) + (L x H))

So now, just put the values inside de formula,

- Pair 1: Length = 3m ; Height = 2m

- Pair 2: Length = 4m ; Height = 2m

- Pair 3: Length = 4m ; Height = 3m

*I know that this pair doesn't have a "real Height" but this doesn't change anything when solving, you can consider the 4m as height and the 3m as length or vice versa, the order of the factors doesn't change the product.

-> At = 2 x ((3 x 2) + (4 x 2) + (4 x 3))
-> At = 2 x (6 + 8 + 12)
-> At = 2 x (26)

-> At = 52 m^2