# Surface Area of Rectangular Prisms

## Surface Area of Rectangular Prisms

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A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles (that is, they have four straight sides and four right angles). Shoeboxes, dice, books: these are all rectangular prisms. The surface area of a rectangular prism is the sum of the areas of all six of its faces. If you know how to calculate the area of a rectangle, you can find the surface area of a rectangular prism. As a formula, this is expressed SA = 2𝑙𝑤 + 2𝑙𝒉 + 2𝑤𝒉.

So, to calculate the surface area of a rectangular prism, follow these steps:

1. Identify the length, width, and height of the rectangular prism. These dimensions of the box will be necessary to calculate the area of each face.
2. Identify the six faces of the rectangular prism. There are two equal faces on the top and bottom of the prism, two equal faces on the front and back, and two equal faces on the sides.
3. Calculate the area of each face by multiplying its length by its width. For example, if a face of the prism has a length of 5 inches and a width of 3 inches, then its area is 5 inches x 3 inches = 15 square inches.
4. Add the areas of all six faces together to find the total surface area of the rectangular prism.

Here's another example: Let's say you order a couch that is delivered in a box 4 meters long, 3 meters wide, and 2 meters tall. We can find the surface area of the box using the following steps:

• The top and bottom faces each have an area of 4 meters x 3 meters = 12 square meters.
• The front and back faces each have an area of 4 meters x 2 meters = 8 square meters.
• The two side faces each have an area of 3 meters x 2 meters = 6 square meters.
• The total surface area of the rectangular prism is the sum of the areas of all six faces: 2(12) + 2(8) + 2(6) = 48 square meters.
• The surface area of the rectangular prism is 48 square meters.