To find the total surface area of a rectangular prism, we can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
Where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length (\( l \)) = 7 cm
- Width (\( w \)) = 3 cm
- Height (\( h \)) = 2 cm
Now, let's calculate each area:
-
Calculate \( lw \): \[ lw = 7 , \text{cm} \times 3 , \text{cm} = 21 , \text{cm}^2 \]
-
Calculate \( lh \): \[ lh = 7 , \text{cm} \times 2 , \text{cm} = 14 , \text{cm}^2 \]
-
Calculate \( wh \): \[ wh = 3 , \text{cm} \times 2 , \text{cm} = 6 , \text{cm}^2 \]
Now, substitute these values into the surface area formula:
\[ \text{Surface Area} = 2(21 , \text{cm}^2 + 14 , \text{cm}^2 + 6 , \text{cm}^2) \]
Calculating the sum inside the parentheses:
\[ 21 , \text{cm}^2 + 14 , \text{cm}^2 + 6 , \text{cm}^2 = 41 , \text{cm}^2 \]
Now, multiply by 2:
\[ \text{Surface Area} = 2 \times 41 , \text{cm}^2 = 82 , \text{cm}^2 \]
Thus, the total surface area of the rectangular prism is:
\[ \boxed{82 , \text{cm}^2} \]