A rectangular prism has a base length of 6 units, base width of 5 units, and height of 4 units. The bases are shaded. The lateral area is . The area of the two bases together is . The total surface area is

1) 88.0 units^2

2) 60.0 units^2

3) 148.0 units^2

Explanation:

1)

The lateral area of a rectangular prism is equal to the sum of the areas of the 4 lateral faces.

Since the areas of 2 opposite faces are equal, the lateral area is:

where are the areas of the two faces.

Here we have:

L = 6 is the length of the base

w = 5 is the width of the base

h = 4 is the height of the prism

So we have:

So the lateral surface area is

2)

The area of one base of the prism is the product of the length of the base and the width:

Where here we have

L = 6 is the length of the base

w = 5 is the width of the base

So the area of 1 base is

And here we have 2 bases, therefore the area of the two bases together is twice the area of the single base:

3)

The total surface area of the prism is given by the sum of the area of the two bases + the lateral area of the prism:

where

is the area of the bases

is the lateral area

Here for this prism we have:

(area of the bases)

(lateral area)

So the total surface area is