Question

find the surface area of the rectangular prism.

Explanation:

Step1: Calculate the area of each pair of faces

The formula for the surface area \(S\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is \(S = 2(lw+lh + wh)\). Here, \(l = 3\) km, \(w=2\) km, \(h = 1\) km.
First, calculate \(lw\): \(lw=3\times2 = 6\) \(km^{2}\).
Then, calculate \(lh\): \(lh=3\times1=3\) \(km^{2}\).
Next, calculate \(wh\): \(wh=2\times1 = 2\) \(km^{2}\).

Step2: Substitute into the surface - area formula

Substitute the values of \(lw\), \(lh\), and \(wh\) into the formula \(S = 2(lw + lh+wh)\).
\(S=2(6 + 3+2)\).
First, calculate the sum inside the parentheses: \(6 + 3+2=11\).
Then, multiply by 2: \(S=2\times11\).

Answer:

\(22\) \(km^{2}\)