To find the surface area of a rectangular prism, you can use the following formula:
\[ \text{Surface Area} = 2lw + 2lh + 2wh \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism. In your case, you have dimensions of 2 cm, 6 cm, and 8 cm.
Let's assign the dimensions as follows:
- Length (\( l \)) = 8 cm
- Width (\( w \)) = 6 cm
- Height (\( h \)) = 2 cm
Now we'll calculate the areas of each pair of faces.
-
Top and Bottom:
The area of the top and bottom faces is calculated as follows: \[ \text{Area (Top and Bottom)} = 2 \times (l \times w) = 2 \times (8 , \text{cm} \times 6 , \text{cm}) = 2 \times 48 , \text{cm}^2 = 96 , \text{cm}^2 \] -
Front and Back:
The area of the front and back faces is calculated as: \[ \text{Area (Front and Back)} = 2 \times (l \times h) = 2 \times (8 , \text{cm} \times 2 , \text{cm}) = 2 \times 16 , \text{cm}^2 = 32 , \text{cm}^2 \] -
Sides:
The area of the side faces is calculated as: \[ \text{Area (Sides)} = 2 \times (w \times h) = 2 \times (6 , \text{cm} \times 2 , \text{cm}) = 2 \times 12 , \text{cm}^2 = 24 , \text{cm}^2 \] -
Total Surface Area: Now, add all the areas together to find the total surface area: \[ \text{Total SA} = \text{Area (Top and Bottom)} + \text{Area (Front and Back)} + \text{Area (Sides)} = 96 , \text{cm}^2 + 32 , \text{cm}^2 + 24 , \text{cm}^2 = 152 , \text{cm}^2 \]
So, the final results are:
- Top and bottom area: 96 cm²
- Front and back area: 32 cm²
- Sides area: 24 cm²
- Total Surface Area: 152 cm²