To calculate the surface area and the areas of each face of a rectangular prism, we need to understand the dimensions you provided:
- Height (h) = 8 feet
- Width (w) = 3 feet
- Length (l) = 12 feet
Areas of Each Face
-
Front face (Width x Height):
\( \text{Area}_{\text{front}} = w \times h = 3 , \text{ft} \times 8 , \text{ft} = 24 , \text{ft}^2 \) -
Back face (Width x Height):
\( \text{Area}_{\text{back}} = w \times h = 3 , \text{ft} \times 8 , \text{ft} = 24 , \text{ft}^2 \) -
Top face (Length x Width):
\( \text{Area}_{\text{top}} = l \times w = 12 , \text{ft} \times 3 , \text{ft} = 36 , \text{ft}^2 \) -
Bottom face (Length x Width):
\( \text{Area}_{\text{bottom}} = l \times w = 12 , \text{ft} \times 3 , \text{ft} = 36 , \text{ft}^2 \) -
Left face (Length x Height):
\( \text{Area}_{\text{left}} = l \times h = 12 , \text{ft} \times 8 , \text{ft} = 96 , \text{ft}^2 \) -
Right face (Length x Height):
\( \text{Area}_{\text{right}} = l \times h = 12 , \text{ft} \times 8 , \text{ft} = 96 , \text{ft}^2 \)
Total Surface Area
To find the total surface area (SA) of the rectangular prism, we sum the areas of all the faces:
\[ \text{Surface Area} = 2 \times (\text{Area}{\text{front}} + \text{Area}{\text{back}} + \text{Area}{\text{top}} + \text{Area}{\text{bottom}} + \text{Area}{\text{left}} + \text{Area}{\text{right}}) \]
Calculating the total:
\[ \text{Surface Area} = 2 \times (24 + 24 + 36 + 36 + 96 + 96) \] \[ = 2 \times (312) = 624 , \text{ft}^2 \]
Summary
- Area of Front Face: \(24 , \text{ft}^2\)
- Area of Back Face: \(24 , \text{ft}^2\)
- Area of Top Face: \(36 , \text{ft}^2\)
- Area of Bottom Face: \(36 , \text{ft}^2\)
- Area of Left Face: \(96 , \text{ft}^2\)
- Area of Right Face: \(96 , \text{ft}^2\)
- Total Surface Area: \(624 , \text{ft}^2\)