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?

648 in.2 648 in. squared 81 in.2 81 in. squared 54 in.2 54 in. squared 27 in.2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The total surface area of a rectangular prism is given by the formula:

2lw + 2lh + 2wh

Given that one face has an area of 6 in^2, 12 in^2 and 9 in^2, we can deduce the dimensions of the prism.

Let's assume the length(l) = 1, width(w) = 2 and height(h) = 3. Then the total surface area is:

2(1*2) + 2(1*3) + 2(2*3) = 4 + 6 + 12 = 22 in^2

So, the total surface area of Jillian's prism is 22 in^2.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the error in my calculation. Let's start over:

Let's denote the dimensions of the rectangular prism as length (l), width (w), and height (h). We are given the areas of three faces:

1. lw = 6 in^2
2. lh = 12 in^2
3. wh = 9 in^2

From the first equation, we can rearrange it to find the value of w in terms of l:

w = 6/l

Now, substitute w = 6/l into the second equation:

l*(6/l)*h = 12
6h = 12
h = 2

Next, substitute h = 2 back into the third equation:

w*2 = 9
w = 4.5

Now we have found the dimensions of the prism:
l = 2, w = 4.5, h = 2

To find the total surface area, use the formula:

2lw + 2lh + 2wh

Substitute the dimensions into the formula:

2(2*4.5) + 2(2*2) + 2(4.5*2)
= 2(9) + 2(4) + 2(9)
= 18 + 8 + 18
= 44 in^2

Therefore, the total surface area of Jillian’s prism is 44 in^2.