The surface area of a prism is the sum of the areas of all the faces.
To find the surface area of a prism, we need to determine the kinds of areas we need to add together.
Consider this cube:
Using the net is useful for seeing exactly what areas need to be added together, but it isn't always this easy to find.
Another way to calculate the surface area of a prism is to calculate all the areas from the dimensions of the prism, without worrying about the exact area of each face.
Since prisms always have two identical base faces and the rest of the faces are rectangles connecting the two bases, we can accurately determine the dimensions of all the faces of a prism from just the dimensions of the base and the height of the prism.
In fact, we can think of all the rectangular faces joining the base faces as a single rectangle that wraps around the prism. One dimension of this rectangle must be the height of the prism. The other dimension of this rectangle will be the perimeter of the base.
With two sides of length 8 and two sides of length 7, the base has a perimeter of 8+7+8+7=30, and multiplying by the height gives us the area 5\times 30 =150.
Adding this area to two copies of the base area tells us the total surface area for the prism: A=2 \times 56 + 150 = 262
We could instead find the area of each of the six rectangles and add them together, but using the perimeter can make some calculations faster.
The following applet demonstrates how to find the surface area of various prisms using a formula.
As we move the sliders the only the dimensions are changing and not the number of faces of the prism.
Find the surface area of the figure shown. Give your answer to the nearest two decimal places.
The surface area of a prism is the sum of the areas of all the faces.
Drawing the net of a prism is useful for seeing exactly what areas need to be added together.