The surface area for a rectangular prism with a square base is given by the formula

The surface area for a rectangular prism with a square base is given by the formula

A

2
s
2
+
4
s
h
.

What is the surface area if

s

2
and

h

4
?

The Correct Answer and Explanation is :

The formula for the surface area ( SA ) of a rectangular prism with a square base is:

[
SA = 2s^2 + 4sh
]

Where:

( s ) is the side length of the square base,
( h ) is the height of the prism.

Given Values:

( s = 2 )
( h = 4 )

Step 1: Substitute the given values into the formula

[
SA = 2(2)^2 + 4(2)(4)
]

Step 2: Simplify each term

First, calculate ( 2(2)^2 ):
[
(2)^2 = 4
]
[
2(4) = 8
]
Next, calculate ( 4(2)(4) ):
[
4 \times 2 \times 4 = 32
]

Step 3: Add the results

[
SA = 8 + 32 = 40
]

Final Answer:

The surface area of the rectangular prism with a square base, where ( s = 2 ) and ( h = 4 ), is 40 square units.

Explanation:

The surface area of a three-dimensional object like a rectangular prism is the total area of all its faces. In the case of a rectangular prism with a square base, there are:

Two square faces at the top and bottom, each with area ( s^2 ).
Four rectangular faces, each with area ( s \times h ).

Thus, the surface area formula is derived by adding the areas of these six faces:

The two square faces contribute ( 2s^2 ) to the surface area.
The four rectangular faces contribute ( 4sh ).

By plugging in the given values for ( s ) and ( h ), we calculated the total surface area, which turns out to be 40 square units. This approach demonstrates how the formula accounts for both the square base and the rectangular sides of the prism.

A

s

h