Question

find the surface area of this rectangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Identify the formula for surface - area of a rectangular prism

The formula for the surface area \(S\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is \(S = 2(lw+lh + wh)\).

Step2: Substitute the given values

Here, \(l = 5\) ft, \(w = 4\) ft, and \(h = 8\) ft. So \(S=2((5\times4)+(5\times8)+(4\times8))\).

Step3: Calculate the products inside the parentheses

\(5\times4 = 20\), \(5\times8 = 40\), and \(4\times8 = 32\). Then \(S = 2(20 + 40+32)\).

Step4: Calculate the sum inside the parentheses

\(20+40 + 32=92\). So \(S = 2\times92\).

Step5: Calculate the final result

\(S = 184\) \(ft^{2}\).

Answer:

\(184\) \(ft^{2}\)