Question

find the surface area of the rectangular prism.
(image of a rectangular prism with dimensions 2 m, 3 m, 3 m)

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. Here, \(l = 2\space m\), \(w=3\space m\), \(h = 3\space m\).

Step2: Calculate each product inside the formula

• Calculate \(lw\): \(lw=2\times3 = 6\)
• Calculate \(lh\): \(lh=2\times3=6\)
• Calculate \(wh\): \(wh = 3\times3=9\)

Step3: Sum the products and multiply by 2

First, sum the products: \(lw+lh+wh=6 + 6+9=21\). Then multiply by 2: \(S=2\times21\)

Answer:

\(42\space m^{2}\)