Question

find the surface area of the rectangular prism. next, find the area of the side rectangles. area of the base and top: 144 cm² area of the side rectangles: ? cm²

Explanation:

Step1: Calculate the area of one pair of side rectangles

The formula for the area of a rectangle is \(A = l\times w\). For the side rectangles with dimensions \(12\) cm (length) and \(2\) cm (width), the area of one rectangle is \(12\times2=24\) \(cm^{2}\). Since there are two such rectangles, their combined area is \(2\times24 = 48\) \(cm^{2}\).

Step2: Calculate the area of the other pair of side rectangles

For the side rectangles with dimensions \(6\) cm (length) and \(2\) cm (width), the area of one rectangle is \(6\times2 = 12\) \(cm^{2}\). Since there are two such rectangles, their combined area is \(2\times12=24\) \(cm^{2}\).

Step3: Sum up the areas of both pairs of side rectangles

Add the results from Step1 and Step2: \(48 + 24=72\) \(cm^{2}\).

Answer:

\(72\)