Question

a rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. what is its surface area? explain or show your reasoning on scrap paper.

Explanation:

Step1: Recall the formula for 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, \(l = 5\space cm\), \(w=2\space cm\), \(h = 2\space cm\).

Step2: Calculate each product inside the formula

• Calculate \(lw\): \(lw=5\times2 = 10\space cm^{2}\)
• Calculate \(lh\): \(lh=5\times2=10\space cm^{2}\)
• Calculate \(wh\): \(wh = 2\times2=4\space cm^{2}\)

Step3: Sum the products and multiply by 2

First, sum \(lw + lh+wh\): \(10 + 10+4=24\space cm^{2}\). Then multiply by 2: \(S=2\times24 = 48\space cm^{2}\)

Answer:

48 square centimeters