Question

surface area = ________

Explanation:

Step1: Recall surface - area formula for rectangular prism

The formula for the surface area \(S\) of a rectangular prism is \(S = 2(ab+bc + ac)\), where \(a\), \(b\), and \(c\) are the lengths of the three sides. Here \(a = 4\) in, \(b = 6\) in, and \(c = 13\) in.

Step2: Calculate \(ab\), \(bc\), and \(ac\)

\(ab=4\times6 = 24\) in², \(bc = 6\times13=78\) in², \(ac = 4\times13 = 52\) in².

Step3: Calculate \(ab + bc+ac\)

\(ab + bc + ac=24 + 78+52=154\) in².

Step4: Calculate the surface area

\(S = 2(ab + bc + ac)=2\times154 = 308\) in².

Answer:

308 in²