To determine the surface area of a rectangular prism with given dimensions, we need to follow these steps:
1. Identify the dimensions of the rectangular prism.
- Length [tex]\( l = 4 \text{ cm} \)[/tex]
- Width [tex]\( w = 2 \text{ cm} \)[/tex]
- Height [tex]\( h = 3 \text{ cm} \)[/tex]
2. Recall the formula for the surface area of a rectangular prism.
The surface area [tex]\( A \)[/tex] can be calculated using the formula:
[tex]\[
A = 2(lw + lh + wh)
\][/tex]
This formula accounts for the area of all six faces of the prism.
3. Calculate each component of the formula.
- The area of the front and back faces ([tex]\( lw \)[/tex]):
[tex]\[
lw = 4 \text{ cm} \times 2 \text{ cm} = 8 \text{ cm}^2
\][/tex]
- The area of the top and bottom faces ([tex]\( lh \)[/tex]):
[tex]\[
lh = 4 \text{ cm} \times 3 \text{ cm} = 12 \text{ cm}^2
\][/tex]
- The area of the left and right faces ([tex]\( wh \)[/tex]):
[tex]\[
wh = 2 \text{ cm} \times 3 \text{ cm} = 6 \text{ cm}^2
\][/tex]
4. Sum these areas.
[tex]\[
lw + lh + wh = 8 \text{ cm}^2 + 12 \text{ cm}^2 + 6 \text{ cm}^2 = 26 \text{ cm}^2
\][/tex]
5. Multiply the sum by 2 to get the total surface area.
[tex]\[
A = 2 \times 26 \text{ cm}^2 = 52 \text{ cm}^2
\][/tex]
Therefore, the surface area of the rectangular prism is [tex]\( 52 \text{ cm}^2 \)[/tex].
Hence, the best answer from the choices provided is:
a. [tex]\( 52 \text{ cm}^2 \)[/tex]
So the correct answer is:
A
