Question

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

Explanation:

Step1: Recall the formula for the 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 \(S = 2(lw+lh + wh)\). Here, \(l = 5\space m\), \(w=2\space m\), and \(h = 7\space m\).

Step2: Calculate each product inside the formula

• Calculate \(lw\): \(lw=5\times2 = 10\)
• Calculate \(lh\): \(lh=5\times7=35\)
• Calculate \(wh\): \(wh=2\times7 = 14\)

Step3: Sum up the products and multiply by 2

First, sum the products: \(lw+lh+wh=10 + 35+14=59\). Then multiply by 2: \(S=2\times59 = 118\)

Answer:

\(118\space m^{2}\)