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    how to find the surface area of a triangular prism

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    Surface Area of Triangular Prism

    The surface area of triangular prism is the total area of all the sides and faces of a triangular prism. The formula for the surface area of a triangular prism is formed by adding up the area of all the rectangular and triangular faces of the prism.

    Surface Area of Triangular Prism

    The surface area of triangular prism is the total area of all its faces. A triangular prism is a prism that has two congruent triangular faces and three rectangular faces that join the triangular faces. It has 6 vertices, 9 edges, and 5 faces. Let us learn more about the surface area of a triangular prism.

    What is the Total Surface Area of a Triangular Prism?

    The surface area of a triangular prism is also referred to as its total surface area. The total surface area of a triangular prism is the sum of the areas of all the faces of the prism. A triangular prism has three rectangular faces and two triangular faces. The rectangular faces are said to be the lateral faces, while the triangular faces are called bases. If the bases of a triangular prism are placed horizontally, they are referred to as the top and the bottom (faces) of the prism, respectively. The surface area of triangular prism is expressed in square units, like, m2, cm2, in2 or ft2, etc.

    Formula for Surface Area of Triangular Prism

    The formula for the surface area of a triangular prism is formed by adding up the area of all the rectangular and triangular faces of a prism. Observe the following figure of a triangular prism to know the dimensions that are considered to frame the formula.

    The formula for the surface area of triangular prism is:

    Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 +S2 + S3)L + bh

    where,

    b is the bottom edge of the base triangle,

    h is the height of the base triangle,

    L is the length of the prism and

    S1, S2, and S3 are the three edges (sides) of the base triangle

    (bh) is the combined area of the two triangular faces [2 × (1/2 × bh)] = bh

    Lateral Surface Area of Triangular Prism

    The lateral surface area of any solid is the area without the bases. In other words, the lateral surface area of a triangular prism is calculated without considering the base area. When a triangular prism has its bases facing up and down, the lateral area is the area of the vertical faces. The lateral surface area of a triangular prism can be calculated by multiplying the perimeter of the base by the length of the prism. The perimeter of the base is the total length of the edges of the base triangle, while the length of the prism is its height. Observe the following figure to understand the lateral surface and the base of a triangular prism.

    Thus, the lateral surface area of triangular prism is:

    Lateral Surface Area = (S1 + S2 + S3) × l = (Perimeter × Length) or LSA = p × l

    where,

    l is the height (length) of a prism

    p is the perimeter of the base

    How to Find the Surface Area of a Right Triangular Prism?

    A right triangular prism has two parallel and congruent triangular faces and three rectangular faces that are perpendicular to the triangular faces. The surface area of a right triangular prism can be calculated by representing the 3-d figure into a 2-d net, which makes it easier to understand. After expanding this 3-d shape into the 2-d shape we get two right triangles and three rectangles. Observe the following figure which shows a right triangular prism. The following steps are used to calculate the surface area of a right triangular prism:

    Step 1: Find the area of the top and the base triangles using the formula, Area of the two base triangles = 2 × (1/2 × base of the triangle × height of the triangle) which simplifies to 'base × height' (bh).Step 2: Find the product of the length of the prism and the perimeter of the base triangle which will give the lateral surface area = (S1 + S2 + h) × l.Step 3: Add all the areas together to get the total surface area of a right triangular prism in square units. This means, total surface area of a right triangular prism = (S1 + S2 + h) × l + bhExample: Find the total surface area of a right triangular prism which has a base area of 60 square units, the base perimeter of 40 units, and the length of the prism is 7 units.Solution: Given, base area = 60 square units, base perimeter = 40 units and length of prism = 7 units

    Thus, the surface area of the right triangular prism, Surface Area = (Perimeter of the base × Length of the prism ) + (2 × Base Area)

    ⇒ SA = (40 × 7) + (2 × 60)

    ⇒ SA = (280 + 120)

    ⇒ SA = 400 square units

    Thus, the surface area of the right triangular prism is 400 square units.

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    Source : www.cuemath.com

    Surface Area of Triangular Prisms

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    Surface Area of Triangular Prisms

    Last Modified: Apr 20, 2021

    [Figure 1]

    Max bought a light prism for his mom for Mother's Day.  He wants to figure out how much wrapping paper is needed to wrap it.  To do this, he needs to figure out the surface area of the gift. The triangular end has a base of 3 cm and height of 4 cm.  The length of each side is 6 cm and the height of the prism (length of the rectangular side) is 8 cm.  What is the surface area of the gift that Max bought for his mom?

    In this concept, you will learn how to calculate the surface area of a triangular prism.

    Finding the Surface Area of a Triangular Prism

    Area is the space that is contained in a two-dimensional figure. Surface area is the total area of all of the sides and faces of a three-dimensional figure.  To find the surface area, the area of each face is calculated and then add these areas together.

    One way to do this is to use a net, since a net is a two-dimensional representation of a three-dimensional solid, or an unfolded picture of a solid.

    What is the surface area of the figure below?

    [Figure 2]

    The net for this triangular prism is as follows:

    [Figure 3]

    Now, let's fill in the measurements for the sides of each face in order to calculate their area.  Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other.

    The formula A= 1 2 bh A=12bh

    is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height. The formula

    A=lw A=lw

    is used to find the area of the three rectangular side faces, where A = area, l = length, and w = width.

    Plugging in the measurements that are given in the net, calculate the area of each face. Remember to use the correct area formula for the triangles and rectangles.

    = Bottom face A= 1 2 bh 1 2 (8)(6)  + 24+ 524 c m 2 Top face A= 1 2 bh 1 2 (8)(6)  + 24+ side A=lw 17×10  + 170 + side A=lw 17×10  + 170 + side A=lw 17×8 136

    Bottom faceTop facesidesidesideA=12bhA=12bhA=lwA=lwA=lw12(8)(6)  +12(8)(6)  +17×10  +17×10  +17×824+24+170 +170 +136= 524 cm2

    When you add these values together, you get a surface area of 524 square centimeters for this triangular prism.

    SA=bh+(s1+s2+s3)H SA=bh+(s1+s2+s3)H

    You can also use one formula to calculate the surface area of a triangular prism which can save time over the process of using a net to derive the areas:

    where b = base; h = height of the triangle; s1, s2, and s3 = the length of each side of the triangle base, and H = the height of the prism (which is the length of the rectangles).

    First, find the area of the two triangular faces. Each face will have an area of

    1 2 bh 12bh

    .  Remember, you can use a formula to calculate the area of a pair of faces. Therefore, you can double this formula to find the area of both triangular faces at once which results in the formula

    2( 1 2 bh) 2(12bh)

    . The 2 multiplied by the

    1 2 12

    equals 1, or cancels each other out, and you're left with

    bh bh .

    Next, you need to calculate the area of each of the rectangular side faces. The length of each rectangle is the same as the height of the prism, so call this

    H H

    . The width of each rectangle is actually the same as the sides of the triangular base. Instead of multiplying the length and width for each rectangle, you can combine this information. Since there are 3 rectangular widths (all equal to the sides of the triangles), multiply the perimeter of the triangular base by the height of the rectangles,

    H H

    , which will give the area of all three rectangles.

    If you put these pieces together—the area of the bases and the area of the side faces—you get this formula:

    SA=bh+(s1+s2+s3)H SA=bh+(s1+s2+s3)H

    where bh = the area of the triangle top and base, and (s1 + s2 + s3)H = the area of the rectangular side faces.

    Remember that the height of the triangular base (h) is not necessarily the same as the height of the prism (H).

    Examples

    Example 1

    Earlier, you were given a problem about the gift Max bought for his mom.

    The triangular end has a base of 3 cm and height of 4 cm. The length of each side is 6 cm and the height of the prism (length of the rectangle) is 8 cm.  What is the surface area of this triangular prism?

    Source : flexbooks.ck12.org

    Surface area using a net: triangular prism (video)

    Learn how to compute the surface area of a triangular prism.

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    Surface area

    Surface area using a net: triangular prism

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    Log in Mr.Phyms SAndhjc 3 years ago

    Posted 3 years ago. Direct link to Mr.Phyms SAndhjc's post “At 1:00 How did he get 1/...”

    At 1:00 How did he get 1/2

    • ERICK270 3 years ago

    Posted 3 years ago. Direct link to ERICK270's post “Like i said to selion if ...”

    Like i said to selion if your talking about how he got the 1/2, thats apart of the formula. Which is, Half of the base times the height, OR, Half the height times the base

    chinjenbin 4 years ago

    Posted 4 years ago. Direct link to chinjenbin's post “How many nets for a prism...”

    How many nets for a prism is there?

    • aryan.batchu09 7 months ago

    Posted 7 months ago. Direct link to aryan.batchu09's post “1 net, chinjenbin”

    1 net, chinjenbin Alexis Vann 3 years ago

    Posted 3 years ago. Direct link to Alexis Vann's post “sooo i ahve a question to...”

    sooo i ahve a question to anyone who whould like too answer me....... HOW DO YOU DO THIS? im so lost its sad can yall please help!

    • ERICK270 3 years ago

    Posted 3 years ago. Direct link to ERICK270's post “A= HB/2 (Half of the base...”

    A= HB/2 (Half of the base times height, Thats the formula for a triangle, i dont have time to give you the other formulas but i hoped this helped.

    Riddick Tayler 3 years ago

    Posted 3 years ago. Direct link to Riddick Tayler's post “i need help on nets and s...”

    i need help on nets and surface area

    • Jaedyn Panduro 2 years ago

    Posted 2 years ago. Direct link to Jaedyn Panduro's post “how come the video will n...”

    how come the video will not play

    • Patria Cordero 4 years ago

    Posted 4 years ago. Direct link to Patria Cordero's post “how do you know if you're...”

    how do you know if you're placing the numbers correctly??

    • Hunter M. Ganey 3 years ago

    Posted 3 years ago. Direct link to Hunter M. Ganey's post “is there a better way to ...”

    is there a better way to explain this like a talk through b/c is still dont understand.

    • Jaiden 2 years ago

    Posted 2 years ago. Direct link to Jaiden's post “Do you always have to mul...”

    Do you always have to multiply by 1/2?

    • Daxton Booth 2 years ago

    Posted 2 years ago. Direct link to Daxton Booth's post “You do if it shows the he...”

    You do if it shows the height of the side

    a year ago

    Posted a year ago. Direct link to %(username)s's post “but how did you get the s...”

    but how did you get the surface area like he numbers on the net by looking at the model that didn't have any numbers on it

    PetitLoiacono,VictoriaIsabel

    a year ago

    Posted a year ago. Direct link to PetitLoiacono,VictoriaIsabel's post “this video make me have m...”

    this video make me have more questions...

    Video transcript

    - What I want to do in this video is get some practice finding surface areas of figures by opening them up into what's called nets. And one way to think about it is if you had a figure like this, and if it was made out of cardboard, and if you were to cut it, if you were to cut it right where I'm drawing this red, and also right over here and right over there, and right over there and also in the back where you can't see just now, it would open up into something like this. So if you were to open it up, it would open up into something like this. And when you open it up, it's much easier to figure out the surface area. So the surface area of this figure, when we open that up, we can just figure out the surface area of each of these regions. So let's think about it. So what's first of all the surface area, what's the surface area of this, right over here? Well in the net, that corresponds to this area, it's a triangle, it has a base of 12 and height of eight. So this area right over here is going to be one half times the base, so times 12, times the height, times eight. So this is the same thing as six times eight, which is equal to 48 whatever units, or square units. This is going to be units of area. So that's going to be 48 square units, and up here is the exact same thing. That's the exact same thing. You can't see it in this figure, but if it was transparent, if it was transparent, it would be this backside right over here, but that's also going to be 48. 48 square units. Now we can think about the areas of I guess you can consider them to be the side panels. So that's a side panel right over there. It's 14 high and 10 wide, this is the other side panel. It's also this length over here is the same as this length. It's also 14 high and 10 wide. So this side panel is this one right over here. And then you have one on the other side. And so the area of each of these 14 times 10, they are 140 square units. This one is also 140 square units. And then finally we just have to figure out the area of I guess you can say the base of the figure, so this whole region right over here, which is this area, which is that area right over there. And that's going to be 12 by 14. So this area is 12 times 14, which is equal to let's see. 12 times 12 is 144 plus another 24, so it's 168. So the total area is going to be, let's see. If you add this one and that one, you get 96. 96 square units. The two magenta, I guess you can say, side panels, 140 plus 140, that's 280. 280. And then you have this base that comes in at 168. We want it to be that same color. 168. One, 68. Add them all together, and we get the surface area for the entire figure. And it was super valuable to open it up into this net because we can make sure we got all the sides. We didn't have to kinda rotate it in our brains. Although you could do that as well. So, with six plus zero plus eight is 14. Regroup the one ten to the tens place, there's now one ten. So one plus nine is ten, plus eight is 18, plus six is 24, and then you have two plus two plus one is five. So the surface area of this figure is 544. 544 square units.

    Source : www.khanacademy.org

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