Question

4 in

5 in
3 in
10 in
10 in
4 in
4 in
5 in
3 in
4 in 13 in 5 in
What is the surface area, in square inches, of the prism?
5 in
10 in

Answer 1

The surface area of the prism, with dimensions provided, is
`\(290 \, \text{in}^2\).` This includes front, back, top, bottom, and side faces, calculated by summing individual face areas.

To find the surface area of the prism, we need to sum up the areas of all its faces.

1. Front and back faces (rectangles):

- Front and back face area = length × height

- Front and back face area =
`\(10 \, \text{in} * 4 \, \text{in} = 40 \, \text{in}^2\)`

2. Top and bottom faces (squares):

- Top and bottom face area = side × side

- Top and bottom face area =
`\(5 \, \text{in} * 5 \, \text{in} = 25 \, \text{in}^2\)`

3. Side faces (rectangles):

- There are four side faces. Two with dimensions
`\(5 \, \text{in} * 10 \, \text{in}\)` and two with dimensions
`\(3 \, \text{in} * 10 \, \text{in}\).`

- Total side face area =
`\(2 * (5 \, \text{in} * 10 \, \text{in}) + 2 * (3 \, \text{in} * 10 \, \text{in})\)`

- Total side face area =
`\(100 \, \text{in}^2 + 60 \, \text{in}^2 = 160 \, \text{in}^2\)`

Now, sum up all the areas to find the total surface area:

`\[ \text{Total Surface Area} = 2(\text{Front and back face area}) + 2(\text{Top and bottom face area}) + (\text{Total side face area}) \]`

`\[ \text{Total Surface Area} = 2(40 \, \text{in}^2) + 2(25 \, \text{in}^2) + 160 \, \text{in}^2 \]`

`\[ \text{Total Surface Area} = 80 \, \text{in}^2 + 50 \, \text{in}^2 + 160 \, \text{in}^2 \]`

`\[ \text{Total Surface Area} = 290 \, \text{in}^2 \]`

Therefore, the surface area of the prism is
`\(290 \, \text{in}^2\)`.