How To Find the Surface Area of a Rectangular Prism
A box is a 6-sided 3-dimensional figure that is very familiar to everyone.Think of a brick or a piece of furniture and you know what it is.The amount of space on the outside of the object is the surface area.It's exactly the same math problem as "How much paper do I need to wrap this shoebox."
Step 1: You can label the length, width, and height of your piece of furniture.
There is a length, a width, and a height to each rectangular prism.Next to three different edges of the shape, write the symbols, and draw a picture.Pick any corner if you're not sure which side to label.Three lines meet at that corner.A box has a base that is 3 inches by 4 inches, and it is 5 inches tall.The long side of the base is 4 inches.
Step 2: Look at the faces.
You need to paint six different faces to cover the whole surface area.Look at a box of cereals and see that there are two faces.The size is the same.There are two faces, one front and one back.The size is the same.There are two faces.The size is the same.If you can't picture it, cut a box apart and put it out.
Step 3: The area of the bottom face is where you should find it.
The bottom is the surface area of just one face.This is the same as every face.The length and width of the rectangle are labeled.Simply divide the two edges together to find the area of the rectangle.Area is the length times width.The area of the bottom face is equal to 12 square inches.
Step 4: The area of the top face is where you can find it.
We already know that the top and bottom faces are the same size.This must also have an area.The top area is also 12 square inches.
Step 5: The area of the back and front faces is where you can find it.
Go back to your diagram and look at the front face, which has one edge labeled width and one labeled height.width times height is the area of the front face.There is also an area of the back.The area of the front is 3 inches x 5 inches, which is 15 square inches.15 square inches is the area of the back face.
Step 6: You can find the area of the left and right faces.
There are two faces left, each the same size.One edge is the length of the prism and the other is its height.The left and right faces have the same area.Our example shows that the area of the left face is 20 square inches.20 square inches is the area of the right face.
Step 7: Add the six areas together.
The area of each of the faces has been found.To get the whole shape, add them all together.You will always get the surface area if you use this formula.Add up all the blue numbers and you have 94 square inches.
Step 8: The formula should be simplified.
Now that you know the surface area of a rectangular prism, you can find it.If you've learned basic math, you can do it faster.The area of a rectangular prism is shown in the equation below.If we combine all the terms, we get the same area.
Step 9: Take the two out.
If you know how to factor in the equation, you can shorten it.
Step 10: You can test it on an example.
The example box has length 4, width 3, and height.Plug these numbers into the formula and you will get 2 x (4x3 + 3x5 + 4x5).That is the same answer we got before.This is a faster way to find the surface area once you've practiced doing these equations.