Question

Follow the steps to find the Surface Area of the square prism.
Shape: Square Prism
3 cm, 3 cm and 3 cm
What is the area?
Top and bottom: [?]
Front and back: [?]
Sides: [?]
Total SA: [?]

Answer 1

To find the surface area of a square prism (also known as a rectangular prism when its base is a rectangle), we follow these steps. However, since the dimensions provided (3 cm, 3 cm, and 3 cm) indicate that it is a cube (which is a special case of a square prism), we will treat it as such.

1. **Identify the dimensions**: All sides are 3 cm.

2. **Calculate the area of each face**:
- **Top and Bottom faces**: Since the top and bottom are squares, the area of one square face is:
\[
\text{Area of one square face} = \text{side}^2 = 3\, \text{cm} \times 3\, \text{cm} = 9\, \text{cm}^2
\]
There are 2 square faces (top and bottom):
\[
\text{Total area for top and bottom} = 2 \times 9\, \text{cm}^2 = 18\, \text{cm}^2
\]

- **Front and Back faces**: Similar to the top and bottom, the front and back are also squares:
\[
\text{Area of one square face} = 3\, \text{cm} \times 3\, \text{cm} = 9\, \text{cm}^2
\]
There are 2 square faces (front and back):
\[
\text{Total area for front and back} = 2 \times 9\, \text{cm}^2 = 18\, \text{cm}^2
\]

- **Side faces**: The left and right sides are also squares:
\[
\text{Area of one square face} = 3\, \text{cm} \times 3\, \text{cm} = 9\, \text{cm}^2
\]
There are 2 square faces (left and right):
\[
\text{Total area for sides} = 2 \times 9\, \text{cm}^2 = 18\, \text{cm}^2
\]

3. **Total Surface Area**:
Now we add the areas of all the faces together:
\[
\text{Total Surface Area (SA)} = \text{Top and Bottom} + \text{Front and Back} + \text{Sides}
\]
\[
\text{Total SA} = 18\, \text{cm}^2 + 18\, \text{cm}^2 + 18\, \text{cm}^2 = 54\, \text{cm}^2
\]

So the answers are:
- Top and bottom: **18 cm²**
- Front and back: **18 cm²**
- Sides: **18 cm²**
- Total Surface Area: **54 cm²**