Question

a rectangular prism has a length of 8 cm, width of 5 cm, and height of 4 cm. what is the surface area of this rectangular prism?
160 cm²
184 cm²
196 cm²
204 cm²

Explanation:

Step1: Recall surface area formula

The surface area \(SA\) of a rectangular prism is given by:
$$SA = 2(lw + lh + wh)$$
where \(l=8\ \text{cm}\), \(w=5\ \text{cm}\), \(h=4\ \text{cm}\)

Step2: Calculate each product term

Calculate \(lw\), \(lh\), \(wh\):

• \(lw = 8 \times 5 = 40\ \text{cm}^2\)
• \(lh = 8 \times 4 = 32\ \text{cm}^2\)
• \(wh = 5 \times 4 = 20\ \text{cm}^2\)

Step3: Sum the product terms

Add the three results:
$$40 + 32 + 20 = 92\ \text{cm}^2$$

Step4: Multiply by 2

Multiply the sum by 2 to get total surface area:
$$SA = 2 \times 92 = 184\ \text{cm}^2$$

Answer:

B. \(184\ \text{cm}^2\)