how to find the area of a prism

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A rectangular prism is a name for a half-dozen-sided 3-dimensional effigy that is very familiar to everybody—a box.^[1] Recall of a brick, or a shoebox, and you know exactly what a rectangular prism is. The area is the amount of space on the outside of the object. "How much paper do I need to wrap this shoebox" sounds a lot less complicated, but it'south exactly the same math problem.

Surface area Help

1
Label the length, width, and height of your rectangular prism. Each rectangular prism has a length, a width, and a height. Depict a picture of the prism, and write the symbols l, w, and h next to three unlike edges of the shape.
- If you're not sure which sides to label, choice whatsoever corner. Label the iii lines that encounter at that corner.
- For instance: A box has a base of operations that measures iii inches by 4 inches, and information technology stands 5 inches tall. The long side of the base is 4 inches, so 50 = 4, w = 3, and h = 5.
2
Await at the half-dozen faces of the prism. To cover the whole surface expanse, you'd need to paint vi dissimilar "faces." Think virtually each i — or find a box of cereal and look at them directly:
- In that location are a meridian and bottom face. Both are the same size.^[2]
- There are a forepart and a dorsum face. Both are the same size.
- There are a left and correct face. Both are the same size.
- If you have problem picturing this, cutting a box apart along the edges and lay it out.^[3]
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iii
Notice the expanse of the bottom face. To start out, allow'southward find the surface area of just one face: the bottom. This is a rectangle, just similar every face. One edge of the rectangle is labeled length and the other is labeled width. To find the expanse of the rectangle, but multiply the two edges together.^[4] Area (bottom border) = length times width = lw.
- Going back to our example, the area of the bottom face is 4 inches 10 iii inches = 12 square inches.
iv
Observe the surface area of the top face. Wait a 2d — nosotros already noticed that the top and lesser faces are the same size. This must too take an area of lw.
- In our example, the acme area is also 12 square inches.
5
Notice the area of the front and back faces. Go back to your diagram and look at the front face: the one with one edge labeled width and one labeled acme. The surface area of the front face = width times height = wh. The area of the back is besides wh.
- In our example, west = 3 inches and h = 5 inches, so the area of the front is 3 inches x five inches =15 square inches. The expanse of the dorsum face is too fifteen foursquare inches.
6
Observe the area of the left and correct faces. Nosotros've simply got two faces left, each the same size. 1 edge is the length of the prism, and one edge is the height of the prism. The expanse of the left face is lh and the expanse of the right face is also lh.
- In our example, l = four inches and h = five inches, so the area of the left confront = four inches x v inches = 20 square inches. The area of the correct face is besides 20 square inches.
7
Add together the six areas together. Now you've institute the area of each of the six faces. Add them all together to get the area of the whole shape: lw + lw + wh + wh + lh + lh. You lot can utilise this formula for any rectangular prism, and you will e'er get the surface area.
- To finish our case, just add up all the blueish numbers above: 12 + 12 + 15 + xv + 20 + twenty = 94 square inches.
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1
Simplify the formula. Y'all now know enough to find the area of any rectangular prism. You can do it faster if you've learned some basic algebra. Get-go with our equation in a higher place: Area of a rectangular prism = lw + lw + wh + wh + lh + lh. If we combine all the terms that are the aforementioned, we get:
- Surface area of a rectangular prism = 2lw + 2wh + 2lh
2
Factor out the two. If you know how to factor in algebra, yous can get in even shorter:
- Expanse of a Rectangular Prism = 2lw + 2wh + 2lh = two(lw + wh + lh).
3
Test it on an example. Let's go back to our example box, with length 4, width 3, and summit 5. Plug these numbers into the formula:
- Area = ii(lw + wh + lh) = two x (lw + wh + lh) = 2 ten (4x3 + 3x5 + 4x5) = 2 10 (12 + 15 + 20) = ii x (47) = 94 square inches. That's the same reply nosotros got before. One time you've practiced doing these equations, this is a much faster way to find the surface area.
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Add together New Question

Question

How exercise I find the surface area of one with no length or is represented by x?

Multiply x by the width and and then by the meridian.
Question

How do I find the edge lengths for a rectangular prism with a surface expanse of 92 m?

You can't notice them without having boosted information.
Question

How practise I find the total expanse of a triangular prism?

Outset off with the formula for the area of a triangle: 1/2bh = a (One half of base times acme equals area.) Also, you'll need to know how to discover the area of a rectangle, lw = a (length times width equals expanse.) Brand a net of the prism. If the length and width of the prism are say, l = 4 and w = 6, the bottom rectangle in the middle should exist 4 ten 6 (expanse = 24 sq. units.). Adjacent, do the other two rectangles (Cheat: They're always the aforementioned area as the base of operations!) Now, discover the expanse of the triangle. Say the height = four. We know w = vi, then we multiply 4 ten half dozen. Now we multiply that by 1/2 (split up by ii). Do the same for the other one, and so add them up.
Question

How do I find the surface expanse of a triangular pyramid?

Find the surface area of each triangle (base x height), then add them together. If all the triangles are congruent, you lot can just discover the expanse of i and multiply information technology by iv.
Question

What is the measure of each edge of a rectangle if the surface area is 600?

Without knowing more about the rectangular prism and the ratio of the side measurements, information technology would be hard to summate. However, if you are talking about a cube in particular, every side would measure 10 units, if the surface area is 600 units squared.
Question

If the surface expanse, length, and width are given, how do I determine the height of a rectangular prism?

Multiply length by width, and double it. That gives you the full area of the top and lesser surfaces of the prism. Subtract that from the full surface area you were given. That leaves you with the total area of the four sides of the prism. Set that number bated for a moment. Add the length and width together and double it. That gives you the perimeter around either the meridian or bottom surface. Divide that perimeter into the total area of the iv sides you figured out a moment agone. That gives you the height.
Question

How do I discover the length (base) of a rectangular prism if I am given the height, width, and total expanse?

Multiply the width past the pinnacle. Double that number. That gives the total surface area of the two smaller ends of the prism. Decrease that effigy from the total surface surface area of the prism. That leaves you with the total expanse of the other four surfaces. Permit's telephone call them the four main surfaces. Add the height to the width and double that figure. That gives you the perimeter effectually the four main surfaces. Separate that perimeter into the full area of the four primary surfaces . That gives you the length of the prism.
Question

How do I write an equation representing the expanse of a rectangle?

Surface area equals length multiplied by width.
Question

How do I determine the area of the left side of a triangular prism when only given the area of the rectangle in forepart?

Yous tin can't without more information.
Question

What is the surface surface area of a right rectangular prism with dimensions of four cm by four cm by half dozen cm?

top and lesser: 16 cm^ii ea. side front and dorsum: 16cm^2 ea. side side and side: 24cm^2 ea. side Total surface surface area = 112 cm^2

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Areas always use "square units," like square inches or foursquare centimeters.^[5] A square inch is but what it sounds similar: a foursquare that's one inch broad and 1 inch long. If a prism has a surface area of l square inches, that means it takes 50 of those squares to cover every surface on the prism.
Some teachers utilize "breadth" or "depth" instead of one of these names. That'due south fine, every bit long every bit you label each side conspicuously.
If you lot don't know which way up the prism is, y'all can call any side the pinnacle. The length is usually the longest side, just fifty-fifty that's non really of import. As long as you lot stick with the same names for the whole problem, yous'll be fine.^[6]

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Commodity Summary X

To find the surface area of a rectangular prism, measure the length, width, and height of the prism. Find the area of the top and bottom faces by multiplying the length and width of the prism. Then, calculate the expanse of the left and right faces by multiplying the width and height. Finally, find the expanse of the front and back faces by multiplying the length and pinnacle of the prism. To find the surface area, simply add all six of these areas together and write your result in square units. If you want to learn how to simplify your formulas to brand them easier to remember, proceed reading the article!

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