Surface area of rectangular prisms | TPT - Free Printable

To solve the problem of finding the surface area of each 3-dimensional rectangular prism (box), we need to calculate the areas of all six faces (top, bottom, front, back, left side, and right side) and then sum them up. The formula for the area of a rectangle is:

\[
\text{Area} = \text{length} \times \text{width}
\]

Step-by-Step Solution for Each Box

#### Box 1:
- Dimensions: \(2 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\)

1. Top and Bottom:
- Area of one face: \(2 \, \text{cm} \times 2 \, \text{cm} = 4 \, \text{cm}^2\)
- Total for top and bottom: \(4 \, \text{cm}^2 + 4 \, \text{cm}^2 = 8 \, \text{cm}^2\)

2. Front and Back:
- Area of one face: \(2 \, \text{cm} \times 2 \, \text{cm} = 4 \, \text{cm}^2\)
- Total for front and back: \(4 \, \text{cm}^2 + 4 \, \text{cm}^2 = 8 \, \text{cm}^2\)

3. Left Side and Right Side:
- Area of one face: \(2 \, \text{cm} \times 2 \, \text{cm} = 4 \, \text{cm}^2\)
- Total for left and right: \(4 \, \text{cm}^2 + 4 \, \text{cm}^2 = 8 \, \text{cm}^2\)

4. Total Surface Area:
\[
8 \, \text{cm}^2 + 8 \, \text{cm}^2 + 8 \, \text{cm}^2 = 24 \, \text{cm}^2
\]

#### Box 2:
- Dimensions: \(3 \, \text{cm} \times 2 \, \text{cm} \times 1 \, \text{cm}\)

1. Top and Bottom:
- Area of one face: \(3 \, \text{cm} \times 2 \, \text{cm} = 6 \, \text{cm}^2\)
- Total for top and bottom: \(6 \, \text{cm}^2 + 6 \, \text{cm}^2 = 12 \, \text{cm}^2\)

2. Front and Back:
- Area of one face: \(3 \, \text{cm} \times 1 \, \text{cm} = 3 \, \text{cm}^2\)
- Total for front and back: \(3 \, \text{cm}^2 + 3 \, \text{cm}^2 = 6 \, \text{cm}^2\)

3. Left Side and Right Side:
- Area of one face: \(2 \, \text{cm} \times 1 \, \text{cm} = 2 \, \text{cm}^2\)
- Total for left and right: \(2 \, \text{cm}^2 + 2 \, \text{cm}^2 = 4 \, \text{cm}^2\)

4. Total Surface Area:
\[
12 \, \text{cm}^2 + 6 \, \text{cm}^2 + 4 \, \text{cm}^2 = 22 \, \text{cm}^2
\]

#### Box 3:
- Dimensions: \(5 \, \text{cm} \times 1 \, \text{cm} \times 1 \, \text{cm}\)

1. Top and Bottom:
- Area of one face: \(5 \, \text{cm} \times 1 \, \text{cm} = 5 \, \text{cm}^2\)
- Total for top and bottom: \(5 \, \text{cm}^2 + 5 \, \text{cm}^2 = 10 \, \text{cm}^2\)

2. Front and Back:
- Area of one face: \(1 \, \text{cm} \times 1 \, \text{cm} = 1 \, \text{cm}^2\)
- Total for front and back: \(1 \, \text{cm}^2 + 1 \, \text{cm}^2 = 2 \, \text{cm}^2\)

3. Left Side and Right Side:
- Area of one face: \(5 \, \text{cm} \times 1 \, \text{cm} = 5 \, \text{cm}^2\)
- Total for left and right: \(5 \, \text{cm}^2 + 5 \, \text{cm}^2 = 10 \, \text{cm}^2\)

4. Total Surface Area:
\[
10 \, \text{cm}^2 + 2 \, \text{cm}^2 + 10 \, \text{cm}^2 = 22 \, \text{cm}^2
\]

#### Box 4:
- Dimensions: \(3 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\)

1. Top and Bottom:
- Area of one face: \(3 \, \text{cm} \times 2 \, \text{cm} = 6 \, \text{cm}^2\)
- Total for top and bottom: \(6 \, \text{cm}^2 + 6 \, \text{cm}^2 = 12 \, \text{cm}^2\)

2. Front and Back:
- Area of one face: \(3 \, \text{cm} \times 2 \, \text{cm} = 6 \, \text{cm}^2\)
- Total for front and back: \(6 \, \text{cm}^2 + 6 \, \text{cm}^2 = 12 \, \text{cm}^2\)

3. Left Side and Right Side:
- Area of one face: \(2 \, \text{cm} \times 2 \, \text{cm} = 4 \, \text{cm}^2\)
- Total for left and right: \(4 \, \text{cm}^2 + 4 \, \text{cm}^2 = 8 \, \text{cm}^2\)

4. Total Surface Area:
\[
12 \, \text{cm}^2 + 12 \, \text{cm}^2 + 8 \, \text{cm}^2 = 32 \, \text{cm}^2
\]

Final Answers:

\[
\boxed{24 \, \text{cm}^2, 22 \, \text{cm}^2, 22 \, \text{cm}^2, 32 \, \text{cm}^2}
\]