To find the surface area of a rectangular prism (or square prism, given the dimensions provided), we can use the formula:
\[ \text{Surface Area (SA)} = 2lw + 2lh + 2wh \]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given the dimensions you provided:
- \( l = 12 \) cm
- \( w = 7 \) cm
- \( h = 10 \) cm
Let's calculate the different areas step by step:
1. Top and Bottom
The top and bottom faces are rectangles with dimensions \( l \) and \( w \).
\[ \text{Area}_{\text{top and bottom}} = 2(l \times w) = 2(12 \times 7) = 2(84) = 168 \text{ cm}^2 \]
2. Front and Back
The front and back faces are rectangles with dimensions \( l \) and \( h \).
\[ \text{Area}_{\text{front and back}} = 2(l \times h) = 2(12 \times 10) = 2(120) = 240 \text{ cm}^2 \]
3. Sides
The side faces are rectangles with dimensions \( w \) and \( h \).
\[ \text{Area}_{\text{sides}} = 2(w \times h) = 2(7 \times 10) = 2(70) = 140 \text{ cm}^2 \]
4. Total Surface Area
Now, we can find the total surface area by adding all individual areas together.
\[ \text{Total SA} = \text{Area}{\text{top and bottom}} + \text{Area}{\text{front and back}} + \text{Area}_{\text{sides}} \]
\[ \text{Total SA} = 168 + 240 + 140 = 548 \text{ cm}^2 \]
Summary
- Top and bottom area: \( 168 \text{ cm}^2 \)
- Front and back area: \( 240 \text{ cm}^2 \)
- Sides area: \( 140 \text{ cm}^2 \)
- Total Surface Area: \( 548 \text{ cm}^2 \)
Thus, the final answer for the surface area of the rectangular prism is 548 cm².