Question

Question
Jillian draws a net for a rectangular prism. One face of the prism has an area of 6 in. 2
. A second face has an area of 12 in. 2
, and a third face has an area of 9 in. 2
. What is the total surface area of Jillian's prism?(1 point)
Responses

81 in.2
81 in.2

54 in.2
54 in.2

27 in.2
27 in.2

648 in.2

Answer 1

To find the total surface area of the rectangular prism, we can use the areas of the three faces provided.

Let's call the dimensions of the rectangular prism:
- Length = \( l \)
- Width = \( w \)
- Height = \( h \)

From the areas given, we can associate them as follows:
1. \( lw = 6 \) in² (first face)
2. \( lh = 12 \) in² (second face)
3. \( wh = 9 \) in² (third face)

To find the total surface area, we can use the formula:
\[
\text{Total Surface Area} = 2(lw + lh + wh)
\]

First, we need to find the individual areas \( lw \), \( lh \), and \( wh \):
- We already know:
- \( lw = 6 \)
- \( lh = 12 \)
- \( wh = 9 \)

Now, we can calculate the total surface area:
\[
\text{Total Surface Area} = 2(6 + 12 + 9)
\]
\[
= 2(27)
\]
\[
= 54 \text{ in}^2
\]

Therefore, the total surface area of Jillian's prism is **54 in²**.