You are looking at your room thinking it would be a lot easier if you could see the dimensions of the room on a flat surface. Actually, we can do just that.
One way to find the surface area of prism is to use a net. A net is a picture of a solid as if it had been flattened out. When you break up a solid into a flat surface, you are able to see all the surfaces and all the sides in two dimensions. Work through the following tabs to learn more.
Net of a Cube
Your Room
The image above represents the net of a cube with sides that all measure 4 inches. How do you think you could use this image to find the surface area of the cube.
There are 6 squares in the net. The area of each square is 16 in2. Since there are 6 identical squares, we can write the following equation:
Surface Area = 16 + 16 + 16 + 16 + 16 + 16 = 96 in2.
Now, let's turn our attention to your room. You are still wondering how to calculate the surface area of your room in order to buy the right amount of paint. Your room has a length of 14 feet, a width of 6 feet, and a height of 10 feet. You get the idea of using a net to find the surface area. The following is the net for the rectangular prism that represents your room.
Now, work through the same process that we used on the cube to find the surface area of your room.
Looking at the net that is created, we have three sets of identical rectangles that are created. We can find the surface area by adding the individual areas of all the rectangles.
Surface Area = 6(10) + 6(10) + 10(14) + 10(14) + 6(14) + 6(14) = 568 ft2
Question
Can you summarize how to find the surface area using nets?
