Question

find the surface area:

Explanation:

Step1: Recall surface - area formula for rectangular prism

The formula for the surface area \(S\) of a rectangular prism is \(S = 2(lw+lh + wh)\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height. Here, \(l = 7\mathrm{cm}\), \(w = 5\mathrm{cm}\), and \(h = 3\mathrm{cm}\).

Step2: Calculate \(lw\), \(lh\), and \(wh\)

\(lw=7\times5 = 35\mathrm{cm}^2\), \(lh = 7\times3=21\mathrm{cm}^2\), \(wh = 5\times3 = 15\mathrm{cm}^2\).

Step3: Calculate \(lw + lh+wh\)

\(lw+lh + wh=35 + 21+15=71\mathrm{cm}^2\).

Step4: Calculate the surface area

\(S = 2\times71=142\mathrm{cm}^2\).

Answer:

\(142\mathrm{cm}^2\)