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Determine the surface area of a rectangular prism with the following dimensions:
Length [tex]\(= 4 \, \text{cm}\)[/tex],
Width [tex]\(= 2 \, \text{cm}\)[/tex],
Height [tex]\(= 3 \, \text{cm}\)[/tex].

A. 52 sq. cm
B. 104 sq. cm
C. 20 sq. cm
D. 290 sq. cm

Please select the best answer from the choices provided.
A
B
C
D



Answer :

GinnyAnswer
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

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