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How to Find the Height of a Rectangular Prism
How to Find the Height of a Rectangular Prism?
To be able to understand how to find the height of a rectangular prism, first let us see what exactly a rectangular prism is. To begin with, let us first understand what a prism is.
Prism:
A prism is not a plane figure. It is a solid three dimensional figure. An object such that all its cross sections in any one direction are same is called a prism. See pictures above:
If the base of the prism is a triangle it is a triangular prism as shown in the first picture.
Similarly a prism with rectangular base is a rectangular prism. A special rectangular prism with square base is called a cube.
A pentagonal prism has base of a pentagon and a hexagonal prism has base of a hexagon. All prisms have two bases of same shape and the sides faces are all rectangles.
Rectangular Prism:
A rectangular prism has all rectangular faces. A rectangular prism has six faces, 8 vertices or corners and 12 edges. It is also called a cuboid. Any pair of opposite faces are same in size and dimensions. Any one such pair of opposite faces is termed as the two bases.
Height of a Rectangular Prism:
The perpendicular distance between the bases is called the height of a rectangular prism. See picture above:
Therefore we see that a rectangular prism primarily has three dimensions, the length and width of the base and the height.
The length and width of base are collectively called the area of the base.
How to Calculate the Height:
The height of a rectangular prism could be calculated by using the following method and the formula given below.
If we know the area of the base and the volume of the prism then the height can be calculated using the formula:
H = Volume/Area of base.
Where, Area of base = length of base x width of base.
For example: Find the height of a rectangular prism with volume = 70 cm^{3} and length and width of base equal to 7 and 5 cm respectively.
Solution: Volume of prism = 70 cm^{3}
Area of base = length of base x width of base
=> Area of base = 7 * 5 = 35 cm^{2}
=> Height = h = volume/area of base = 70/35 = 2cm
=> Therefore answer = 2 cm.
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From Yahoo Answers
Question:Please help figure out this answer! The question says: A rectangular prism has a volume of 120cm^3. Its length is 5 cm and its width is 8 cm. What is the prisms height? thanks :)
Answers:divide 120 by the base which is 40 the answer is 3
Answers:divide 120 by the base which is 40 the answer is 3
Question:Here's the example I'm given:
http://learn.flvs.net/webdav/educator_math2_v5/module10/imagmod10/10_03a_03.gif
To find the surface area, visualize the net for this figure.
The net consists of a large rectangle (the lateral faces) with sides of 12 cm and the perimeter of the base (5cm +5 cm +8 cm +8 cm = 26 cm). The area of the lateral faces would be
12 cm X 26 cm = 312 square cm
The bases of the prism are rectangles with length and height of 8 cm and 5 cm. The area of this would be
8 cm X 5 cm = 40 square cm
Adding the lateral area and 2 bases together will reveal the surface area.
312 sq cm + 2(40 sq cm) = 392 sq cm
I dont really get it. Can somebody help me find a way to remember this, and explain it? Thanks. http://i31.tinypic.com/153ty7l.png
Answers:Just so you know, your link led to a complaint page because the system with the example expects a "cookie" which, of course, was only set on your computer. But this example is fairly straightforward, though the term "net" is a little odd. What they are doing is "unfolding" the sides of the prism to calculate the surface area. The four sides ("lateral faces") unfold into one large rectangle, and that leaves the top and bottom ("bases") to be added in. So they calculate the area of the lateral sides (height times the perimeter of the base = 312) and then add the area of the two bases, each being length x width (which gives the 2 * 40). Here's another, equivalent way to look at it: take the three dimensions of the rectangular as x, y, and z. For each pair of measurements, there will be two opposite faces that consist of rectangles with that pair of dimensions. So the area is 2(xy + xz + yz). In the example, x=5, y=8, z=12 (or you can assign them in any other order and it will come out the same). So the surface area is 2 (5*8 + 5*12 + 8*12) = 2 (40 + 60 + 96) = 2 * 196 = 392 Their approach, unfolding the sides and then adding the top and bottom, just collects the areas of the sides in a different order. You're still adding up six rectangles; it's just that they've stuck four of them together in one step.
Answers:Just so you know, your link led to a complaint page because the system with the example expects a "cookie" which, of course, was only set on your computer. But this example is fairly straightforward, though the term "net" is a little odd. What they are doing is "unfolding" the sides of the prism to calculate the surface area. The four sides ("lateral faces") unfold into one large rectangle, and that leaves the top and bottom ("bases") to be added in. So they calculate the area of the lateral sides (height times the perimeter of the base = 312) and then add the area of the two bases, each being length x width (which gives the 2 * 40). Here's another, equivalent way to look at it: take the three dimensions of the rectangular as x, y, and z. For each pair of measurements, there will be two opposite faces that consist of rectangles with that pair of dimensions. So the area is 2(xy + xz + yz). In the example, x=5, y=8, z=12 (or you can assign them in any other order and it will come out the same). So the surface area is 2 (5*8 + 5*12 + 8*12) = 2 (40 + 60 + 96) = 2 * 196 = 392 Their approach, unfolding the sides and then adding the top and bottom, just collects the areas of the sides in a different order. You're still adding up six rectangles; it's just that they've stuck four of them together in one step.
Question:I have a formula of SA=LA+2B how would u do it that way
Answers:(5x6)x2=60 (5x3)x2=30 (6x3)x2=36 60+30+36=126 126 is your answer
Answers:(5x6)x2=60 (5x3)x2=30 (6x3)x2=36 60+30+36=126 126 is your answer
Question:A rectangular prism has dimensions 4 by 6 by x. If the total surface area of the prism is 248 square units, what is the value of x?
Answers:surface area of a rectangular prism is... A=(L*H*2)+(L*W*2)+(H*W*2) A=area L=length W=width H=height now the reason for that is look at this image http://demonstrations.wolfram.com/EstimatingTheSurfaceAreaAndVolumeOfARectangularPrism/HTMLImages/index.en/popup_1.jpg the blue color is the length and width, and because there are 2 sides of that exact same length and width, is why you multiply it by 2 same goes with the purple color side and tan color side. the reason why you want to add all 3, is because we are dealing with surface area 4 and 6 doesnt say what it is, so we can pick between Length or Width or Height, because it really doesnt matter, you have to eventually multiply them all... i know how i worded it sounds weird, because it sounds weird to me LOL... so, L has to be in L*H*2, and L*W*2.. same goes with W, W*L*2 (like already mentioned, W*L*2 is same as L*W*2), then W*H*2.. and same goes with H (which we already mentioned with the other 2, however its H*W*2 (same as W*H*2), and H*L*2 (same as L*H*2) just tryin to break it down for you lol.. i know all these big blocks of texts can be annoying, but its not really that difficult with all that said, we can make up weather 4=Length or Width or Height, and same goes for 6, if you dont understand why, just reread my block of texts so if A=248 L=lets say 4 W=lets say 6 H=lets say X A=(L*H*2)+(L*W*2)+(H*W*2) plug in the values we know 248=(4*x*2)+(4*6*2)+(x*6*2) simplify 248=8x+48+12x simplify further by combinding the x values 248=20x+48 subtract 48 on both sides of equation 200=20x divide 20 on both sides of equation to get x value by itself 10=x then if you plug in 10 for the value of x, into the original equation A=(L*H*2)+(L*W*2)+(H*W*2) the surface area should come out to 248 its always good to double check work
Answers:surface area of a rectangular prism is... A=(L*H*2)+(L*W*2)+(H*W*2) A=area L=length W=width H=height now the reason for that is look at this image http://demonstrations.wolfram.com/EstimatingTheSurfaceAreaAndVolumeOfARectangularPrism/HTMLImages/index.en/popup_1.jpg the blue color is the length and width, and because there are 2 sides of that exact same length and width, is why you multiply it by 2 same goes with the purple color side and tan color side. the reason why you want to add all 3, is because we are dealing with surface area 4 and 6 doesnt say what it is, so we can pick between Length or Width or Height, because it really doesnt matter, you have to eventually multiply them all... i know how i worded it sounds weird, because it sounds weird to me LOL... so, L has to be in L*H*2, and L*W*2.. same goes with W, W*L*2 (like already mentioned, W*L*2 is same as L*W*2), then W*H*2.. and same goes with H (which we already mentioned with the other 2, however its H*W*2 (same as W*H*2), and H*L*2 (same as L*H*2) just tryin to break it down for you lol.. i know all these big blocks of texts can be annoying, but its not really that difficult with all that said, we can make up weather 4=Length or Width or Height, and same goes for 6, if you dont understand why, just reread my block of texts so if A=248 L=lets say 4 W=lets say 6 H=lets say X A=(L*H*2)+(L*W*2)+(H*W*2) plug in the values we know 248=(4*x*2)+(4*6*2)+(x*6*2) simplify 248=8x+48+12x simplify further by combinding the x values 248=20x+48 subtract 48 on both sides of equation 200=20x divide 20 on both sides of equation to get x value by itself 10=x then if you plug in 10 for the value of x, into the original equation A=(L*H*2)+(L*W*2)+(H*W*2) the surface area should come out to 248 its always good to double check work
From Youtube
Finding the Volume of a Rectangular Prism :WEBSITE: www.teachertube.com This is a mini clip which can be used as a guiding tool for students who may need to review how to determine the volume of a rectangular prism.
How to find the Surface Area of a Rectangular Prism :Step by step procedure to finding surface area of a rectangular prism.