Question

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

Answer 1

88 units squared

60 units squared

148 units squared

Answer 2

1) 88.0 units^2

2) 60.0 units^2

3) 148.0 units^2

Step-by-step 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:

`A_L=2A_1 + 2A_2`

where
`A_1,A_2,A_3` 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:

`A_1=L\cdot h = (6)(4)=24`

`A_2=w\cdot h =(5)(4)=20`

So the lateral surface area is

`A_L = 2(24)+2(20)=88`

2)

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

`A=L\cdot w`

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

`A=(6)(5)=30`

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

`A_b=2A=2(30)=60`

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:

`A=A_b+A_L`

where

`A_b` is the area of the bases

`A_L` is the lateral area

Here for this prism we have:

`A_b=60` (area of the bases)

`A_L=88` (lateral area)

So the total surface area is

`A=60+88=148`