Use the image to answer the question.
An illustration shows an unfolded version of a rectangular prism.
A large vertical rectangle is divided into four stacked horizontal rectangles labeled as side, bottom, side, and top, all with common dashed lines in between them. The second rectangle, labeled as bottom, shows a length of 12 centimeters and a width of 7 centimeters. There are two additional rectangles adjoined to both sides of the second rectangle, with common dashed lines in between them. These two adjoined rectangles are labeled as side, each with a width of 3 centimeters.
Find the lateral surface area of the rectangular prism represented by the given net.
page 13 of 14
To find the lateral surface area of the rectangular prism, we need to find the area of the four lateral faces which are the sides of the prism.
The lateral surface area of a rectangular prism can be calculated by adding the areas of the four sides:
Lateral Surface Area = 2 * (side1 + side2 + side3 + side4)
In the given net, we can see that side1 and side2 have dimensions of 12 cm (length) and 3 cm (width). Therefore, the area of side1 and side2 would be:
Area of side1 and side 2 = 12 cm * 3 cm + 12 cm * 3 cm = 72 cm^2
Similarly, side3 and side4 have dimensions of 7 cm (length) and 3 cm (width). So, the area of side3 and side4 would be:
Area of side3 and side 4 = 7 cm * 3 cm + 7 cm * 3 cm = 42 cm^2
Now, the lateral surface area of the rectangular prism would be:
Lateral Surface Area = 2 * (72 cm^2 + 42 cm^2) = 2 * 114 cm^2 = 228 cm^2
Therefore, the lateral surface area of the rectangular prism represented by the given net is 228 square centimeters.