The surface area of a rectangular prism calculator gives us the answer:Ī = 2 × l × w + 2 × l × h + 2 × w × h = 2 × 8 ft × 6 ft + 2 × 8 ft × 5 ft + 2 × 6 ft × 5 ft = 236 ft².īut that is the surface area of the entire prism, and we don't want to tile it all around. " And we're done, aren't we?" Well, not exactly. And that is exactly what we should do now: set c = 5 ft, which is the depth of the pool or the height of the prism. We're left with the depth of our pool and the number c in the calculator. Note that it doesn't matter in which order we put them it only translates to looking at the pool from another angle and doesn't change its surface area.
Since we're using l and w as the base edges, we can use these numbers in the calculator above and set l = 8 ft and w = 6 ft. Now that we have the numbers let's try to put them in terms of the notation we've used above.įirstly, the sides of the base of our pool are its length and width, which in our case are 8 ft and 6 ft, respectively. Say that the pool has a length of 8 feet, a width of 6 feet, and is 5-foot-deep. Okay, we know it's hard to keep your eyes away from the floaty unicorn, but let's get back to the problem at hand! Observe that, together with the base area, this allows us to translate the surface area of a rectangular prism formula intoĪ = 2 × A_b + A_l = 2 × l × w + 2 × l × h + 2 × w × h. All in all, we obtain that the lateral area, or A_l as we call it, is Also, the other side of one of the pairs is equal to the first base edge, say l, and the other is equal to the length of the second one, which is w. All of those have one side equal to h, the lateral edge (or the height) of the prism. What is more, among the four, there are two pairs of identical ones (the front and back wall and the left and right wall). We have four faces contributing to that number, and all of them are rectangles. Piece of cake, wasn't it? Well, let's now try to do something a little bit more complicated and move on to the lateral area. And that is precisely the formula for the base area: With our notation, it is a rectangle with sides l and w, so its area is l × w. Now, let's use that information to study the base of our prism. Recall that all the faces in our calculator are rectangles, and, as mentioned in the rectangle area calculator, they are calculated by multiplying the side lengths. Surface_area = 2 × base_area + lateral_area, Therefore, since the solid has two bases (the bottom one and the top one), the surface area of a rectangular prism formula is as follows: On the other hand, A_l denotes the lateral area, meaning the total area of the four lateral faces. Note that A_b denotes the surface area of a single base of our prism.
SURFACE AREA OF A RECTANGULAR PRISM FORMULA HOW TO
Time to put the high-brow words aside and focus on how to find the surface area of a rectangular prism. Lastly, the sides of each rectangle are called edges (again divided into base edges and lateral edges).
The bottom and top faces of the box are called bases, and each of the other four is called a lateral face. Note that this, in particular, means that there are three pairs of identical faces placed on opposite sides of the solid.Īlso, as with any other scientific definition, there are a few fancy names associated with the prism. Well, that is a rectangular prism! Or do you remember those drawings of houses that we did in kindergarten? Remove the angular roof, and you're left with another example of a rectangular prism.įormally (mathematically), a right rectangular prism is a solid where all six sides are rectangles that are perpendicular to one another.
SURFACE AREA OF A RECTANGULAR PRISM FORMULA FULL
A regular, rectangular box, just like the ones you see in the supermarket, full of whatever products. Before we see what the surface area of a rectangular prism is, we should get familiar with the prism itself.
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