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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the rectangular prism, we need to add up the areas of all six faces.

Let the length of the rectangular prism be l, width be w, and height be h.

Given:
One face area = 6 in^2
Second face area = 12 in^2
Third face area = 9 in^2

Since the area of one face is lw = 6 in^2:
l * w = 6

Since the area of the second face is lw = 12 in^2, and we already know l * w = 6 in^2, then:
l * w = 12

So, the dimensions l, w of the prism are 2 and 3 (l = 2, w = 3 or l = 3, w = 2).

Now we need to find the height h:
From one face area = lw = 6 in^2, we know the product of the length and width is 6.
Since one face area = 6, we can say l = 2 and w = 3.
We also know the area of the third face = lh = 9 in^2:
l * h = 9
2 * h = 9
h = 4.5
Therefore, the dimensions of the prism are length (l) = 2, width (w) = 3, height (h) = 4.5.

The total surface area of the rectangular prism is given by:
2lw + 2lh + 2wh = 2(2 * 3) + 2(2 * 4.5) + 2(3 * 4.5) = 4 + 18 + 27 = 49 in^2

Therefore, the total surface area of Jillian's prism is 49 square inches.

Answer 2

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. squared

27 in.2
27 in. squared

648 in.2
648 in. squared

54 in.2
54 in. squared

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of Jillian's prism, we need to consider that a rectangular prism has 6 faces: top, bottom, front, back, left side, and right side.

Given:
Area of one face = 6 in^2
Area of a second face = 12 in^2
Area of a third face = 9 in^2

Let's denote the lengths of the rectangular prism as l, w, and h.

The areas of the faces can be described as follows:
Top and Bottom Faces (l * w) = 6 in^2
Front and Back Faces (l * h) = 12 in^2
Left and Right Faces (w * h) = 9 in^2

From the given areas, we have:
l * w = 6
l * h = 12
w * h = 9

By solving these equations, we find that l = 2, w = 3, and h = 4.5

The total surface area of the prism is given by:
2lw + 2lh + 2wh
= 2(2*3) + 2(2*4.5) + 2(3*4.5)
= 12 + 18 + 27
= 57 in^2

Therefore, the total surface area of Jillian’s prism is 57 in^2.