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Lecture Comments (1)

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Post by Arpana Duggal on June 30, 2012

Hi, this section 9 is suppose to be marked IX instead of XI (11). Just letting you know.

Volume of a Triangular Prism

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  • Volume of a Prism = Area of the base × Height
  • Volume of a Triangular Prism = Area of triangle × Height

Volume of a Triangular Prism

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Volume of a Triangular Prism 0:06
    • Volume of a Triangular Prism: Formula
  • Extra Example 1: Find the Volume of the Triangular Prism 2:42
  • Extra Example 2: Find the Volume of the Triangular Prism 7:21
  • Extra Example 3: Find the Volume of the Solid 10:38

Transcription: Volume of a Triangular Prism

Welcome back to Educator.com.0001

For the next lesson, we are going to go over volume of a triangular prism.0002

Volume remember is the measure of all the space inside the prism or the solid.0010

Whenever you take a solid, a three-dimensional object,0021

and you fill it with something, you are measuring volume, all the space inside.0025

Just like for the rectangular prism, to find the volume of a triangular prism,0033

you are going to find the area of the base and multiply that to the height.0039

For a triangular prism, we know that the bases are triangles0044

which is why it is called the triangular prism.0049

When we find the area of the base, we are finding the area of the triangle.0052

The height, be careful with the height because... the triangle has a height.0058

But the height that we have to use here, it is not the height for the triangle.0065

It is the height of the prism; it is the height between the two bases.0070

Let me explain that a little bit more.0076

For a volume of a prism, it is always area of the base,0082

whatever the base is, times the height of the solid, of the prism.0086

Since we are dealing with triangular prisms, the area of the base is going to be the area of the triangle.0093

Here is the base.0102

We know that the area of a triangle is 1/2 base times height.0105

That is the area of a triangle.0112

Be careful; like I said, this height is not the same as this height.0115

The height here, this is just talking about the triangle; only the triangle.0119

The height here is going to be the height of the prism.0125

We know that this a base and this is a base.0128

The height is going to measure the distance between the two bases, this base here to the back base.0133

This right here is going to measure the height here.0143

Again area of the base which is the triangle, 1/2 base times height, times the height of the prism.0149

That is the volume of this triangular prism.0157

Here if you look at our example, this is triangular prism.0164

It might be a little bit difficult to see.0171

But just think of this as the top; that is the peak.0172

That is the top part; this bottom, that is the ground.0178

This triangular prism, the base would be the triangles.0189

Again just to review over what makes a prism,0198

remember that we have two bases that are both parallel and congruent0203

which will be these two triangles on opposite sides here.0210

There is two sides; there is two bases always for every prism.0213

They are always going to be the non-rectangle.0217

If you have a prism and you have couple of different pairs that can be opposite, parallel, and congruent,0220

you always look for the ones that are not rectangles because the bases are those.0231

All the rest of the sides, all the lateral faces, the sides that are not bases,0239

the lateral faces are going to be rectangles.0244

If you look here, see that is the rectangle.0246

This is a rectangle; and then the bottom side will be a rectangle.0249

Again those are my bases.0256

To find the volume, we are going to find the area of the base.0260

For the area of the base, I can label that as capital B.0267

If I do a lowercase B, then that is talking about just a base, just one side.0271

That is considered the base.0276

But a capital B represents the area of a base like a side.0277

That is called the base; capital B is for area of the base.0282

Then times the height.0287

You can also think of the volume of a prism in this formula right there.0288

Again triangular prism, our base is going to be the triangle.0295

1/2 base times height of the triangle times the height of the prism.0301

I am going to just put P here for prism.0308

That is the height of the prism.0312

That is just to show what type of height it is.0313

For my triangle, my base and my height; remember that between these two, base and the height,0320

whenever you find the area of a triangle, the base and the height have to be perpendicular.0329

For this, one of these will be considered the base.0333

The other one will be considered the height.0337

6 and 8 will be my base and my height.0339

Just remember that the base and the height, they have to be perpendicular to each other.0343

1/2 times 6 times 8... I don't like the...0350

You can think of it that way; 1/2 base times height.0360

The height of the prism again is going to be the measure between the two bases.0363

This is going to be the height of the prism; that is 10.0370

1/2 times 6; 1/2 times 6; think of this as 6/1.0378

Half of 6 is 3; you can also do 1/2 times 6.0386

You are going to multiply whenever you do fractions.0390

1 times the 6; you are going to multiply the top numbers together.0392

Then multiply the bottom numbers together.0396

1 times 6 is 6; over... 2 times 1 is 2; 6/2 is 3.0398

3 times 8 is 24; times that by 10.0405

Remember whenever you multiply a number times 10,0415

you are just going to add a 0 at the end of it like that.0417

Our units is centimeters.0424

Remember whatever you do with volume, it is always units cubed.0426

Meaning to the 3rd power; centimeters cubed, 3rd power.0430

That is the volume of this triangular prism.0436

The next example, again we have volume being the area of the base0443

Capital B for area of the base times the height of the prism.0449

The reason why I am just adding it like this is because0456

this is the formula for any type of prism, not just triangular prism.0458

But it could be hexagonal prism; it could be rectangular prism.0462

Any type of prism, this will be the volume.0470

Just whatever the base is, you are going to find the area of that base.0473

Then multiply to the height of the prism.0477

Here triangular prism, this is the area of the triangle.0480

Let's see; 1/2 base times height; it is going to be 1/2 times the base.0487

If you look at the triangle, there is a triangle.0493

I am just showing you in red what the base is.0498

The height of the triangle is 2; the base is 4.0505

Remember the base and the height of the triangle0509

when you do 1/2 base times height, they always have to be perpendicular.0512

This is 2; this is 4; base times the height of 2.0517

If you multiply these three numbers together, you are going to get the area of that triangle.0525

Multiply it to the height of the prism, between the two bases.0531

See how the front face is the base and the back is the base.0538

Between them, the distance is 8; that is the height.0543

Half of 4; half of 4 is 2; 2 times 2 is 4.0553

The area of the base is actually 4 inches squared because that is the area.0563

It is always the unit squared.0569

4 times 8; volume is 32; inches to the 3rd power; units cubed.0571

That is the volume of this triangular prism.0588

This side right here is given to you, 5 inches.0594

But that is just there to throw you off.0599

Just make sure you don't use this.0602

Even if they give you more measures than you need, you don't have to use it all.0605

You don't need this side right here unless you need that for the area of the triangle.0612

But remember the base and the height have to be perpendicular.0618

That has nothing to do with the base and the height.0621

That is just the length of the side right here; don't worry about that.0624

1/2 base times the height times the height of the prism which is 8.0632

The third example, we are going to find the volume of this solid.0638

Here we have a rectangular prism and a triangular prism.0643

We have to find the volume separately.0649

We are going to find the volume of the rectangular prism.0651

Then find the volume of the triangular prism.0654

Then we are going to add them together.0658

Volume of... let's do the rectangular prism first.0663

For the rectangular prism, volume is remember the area of the base times the height.0669

Let's say if we label the top and the bottom as the base, then we know that0690

this right here is 8 meters because that is the same as that right there.0700

The area of the base is 8 times this right here which is 8.0708

Remember anytime you find the volume of a prism, it is going to be0718

the area of the side base times the height of the prism.0721

For this rectangular prism, the base is going to be 8 times the 8; 8 times 8.0735

The height is this right here; 7 meters.0744

8 times 8 is 64; times 7; 64 times 7.0754

4 times 7 is 28; 6 times 7, 42; 44; 448.0764

Volume, remember the units, it is going to be meters cubed, to the 3rd power; units cubed.0781

We found the volume of the rectangular prism.0794

Now I have to find the volume of this triangular prism up here.0797

For the triangular prism, I am just going to put tri for triangular prism.0802

The volume again same thing, area of the base times the height.0808

We know that the base in this one is the triangle.0813

There is our base, this triangle here.0818

To find the area of that, it is going to be0821

1/2 times the base of the triangle which is that right there.0824

Remember the height of the triangle has to be perpendicular to that base.0835

If this is the base 8, then the height is going to be 5 because that is what is perpendicular.0839

See that?--it is 5.0847

These three numbers multiplied together is going to give us the area of that triangle.0851

Then we have to find the height of this prism.0855

The height of the prism is going to be the distance between the two bases.0862

If this triangle, the face in the front is the base, then the back triangle is also the base.0869

The height of the prism is the distance between the two.0880

How far apart are these bases?--that would be this right here.0885

This is actually the height of the prism.0891

We know that this side is the same as this.0895

The height of that is going to be 8 or 8 meters.0898

Half of 8; 1/2 times 8; we know that half of 8 is 4.0906

4 times 5 is 20; remember this; that is the area of the triangle.0912

Multiply that to the height of the prism.0919

The volume of this is... 2 times 8 is 16.0923

Then I am going to just place a 0 right there.0930

It is 160 meters cubed; that is the volume of this triangular prism.0933

Now I have to add them together.0941

448 meters cubed plus 160 meters cubed is going to be... 8.0945

This is 10; 4, 5, 6; 608 meters cubed; cubed to the 3rd power.0958

This is the volume of this solid here.0968

That is it for this lesson; thank you for watching Educator.com.0973