Question

a cardboard box is 12 inches (in.) wide, 16 in. long, and 14 in. high. what is the total surface area of the box?

Explanation:

Step1: Recall the formula for the surface area of a rectangular prism

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

Step2: Substitute the given values into the formula

Given \(l = 16\), \(w=12\), and \(h = 14\).
First, calculate \(lw\): \(lw=16\times12 = 192\)
Next, calculate \(lh\): \(lh=16\times14=224\)
Then, calculate \(wh\): \(wh=12\times14 = 168\)
Now, find \(lw+lh+wh\): \(192 + 224+168=584\)
Finally, find \(S\): \(S = 2\times584\)

Answer:

\(1168\) square inches.