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Area of a Triangle

• Area of a Triangle = (base × height)/2

Area of a Triangle

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
• Area of a Triangle 0:05
• Area of a Triangle: Equation and Example
• Extra Example 1: Find the Area of the Triangles 1:31
• Extra Example 2: Find the Area of the Figure 4:09
• Extra Example 3: Find the Area of the Shaded Region 7:45

Transcription: Area of a Triangle

Welcome back to Educator.com.0000

For the next lesson, we are going to go over the area of a triangle.0002

The formula for the area of a triangle is base times height divided by 2 or 1/2 base times height.0008

Here we have a parallelogram.0018

We know that area of a parallelogram is base times height.0021

Here is a rectangle; the area of this is base times height.0029

If I take this parallelogram and I cut it in half, let's say I cut it this way.0035

Then I have two equal halves; I then have a triangle.0043

One of these triangles would be the whole thing, the whole parallelogram, cut into half.0049

This triangle is base times height divided by 2 because I cut it in half.0058

Same thing here.0066

If I take this rectangle and I cut it in half, I am going to get the triangle.0067

That is why the formula for the area is the base times the height divided by 2.0080

Because it is cut in half; base times height, cut in half.0085

Here are a couple of triangles; we are going to find the area.0095

Again remember area is how much space it is covering.0098

We are going to see how much space this triangle is covering.0101

The area of this triangle has a formula of 1/2 base times height or base times height divided by 2.0110

The base we know is 8; remember base times height.0122

It is still the same as the previous lesson when we talked about parallelograms.0126

The base and the height have to still be perpendicular.0131

When we talk about height, we are talking about the perpendicular height from the highest point to the lowest point.0134

It has to be perpendicular; they have to be perpendicular to each other.0141

The base is 8; the height is not this side, this side right here.0146

It has to be this height; that is 6 inches.0153

It is all of that divided by 2.0160

8 times 6 is 48; divided by 2.0164

This looks like a fraction; but it is also divide.0169

48 divided by 2 is 24; our units is in inches; it is inches squared.0172

Because it is area, any time you are talking about area, it is always units squared.0184

That is the area of this triangle here.0190

The next one, area equals the base times the height divided by 2.0194

This looks like half of our rectangle we drew.0203

That rectangle; it is half of that.0207

Base times the height; the base is 5; the height is 10.0212

We know that is 10 because it is perpendicular.0219

But because we are only looking at half of it, the triangle part, we are going to divide that by 2.0223

Area equals 50 divided by 2; 50 in half is 25; centimeters squared.0229

Next, find the area of the figure.0248

There is no formula to figure out the area of this whole thing in one formula.0255

We have to break this up into two parts.0262

We know the area of a triangle.0265

We know the formula for the area of this rectangle.0270

If I put it together, I am going to add the area of this triangle to the area of this rectangle.0274

First the area of the triangle.0290

I am going to do a triangle plus a rectangle is going to equal...0293

All this plus all that is going to equal triangle with that.0301

Area of the triangle, triangle first, is 1/2 base times height or base times height divided by 2.0313

The base is 6 right here.0329

Even though the base is not the one on the bottom,0332

this has to be the base because the height and the base have to be perpendicular.0337

If you want, you can just redraw this triangle so that this becomes the base like that.0344

If this is 6, this side is this side right here.0352

Then that is the triangle; this can be 8.0357

But just because it is moved, it is rotated where this is right here, it doesn't change the area.0362

Base is 6; the height is 8 meters; divided by 2.0373

6 times 8 is 48; divided by 2; half of 48 is 24.0382

That is meters squared.0391

For the rectangle... because this is only the area of this.0395

To find the area of the rectangle, it is just base times the height and not divided by 2.0400

The base is 10; the height is 6; they are perpendicular; that is fine.0408

This is 60 meters squared; remember what you have to do.0422

Take the area of the triangle; add it to the area of the rectangle.0429

This is the rectangle.0435

It is going to be 24 meters squared plus 60 meters squared.0442

Together it is going to be 84 meters squared.0452

That is the area of this figure right here.0458

For this one, we are going to find the area of the shaded region.0467

This is different than the previous one because we had0472

two shapes that were put together to make up a figure.0476

This is different; this is overlapping.0480

Here we are just finding only the area of this right here, all this blue.0484

In this case, let's say we have a paper.0492

This blue, this whole rectangle here, let's say that is our piece of paper.0499

We have a piece of paper that is going to be blue like that.0508

We are going to take scissors and we are going to cut out a piece of it; that triangle piece.0512

Don't you remove some of the area?--you are uncovering some of the area.0519

You have to subtract the triangle there; the area of this minus the triangle.0524

That is going to give you that whole thing, cut out the triangle, all of this.0536

The previous one we had to add because they were put together.0549

But this one, we are going to subtract.0552

The area of this rectangle first; a rectangle.0555

We know that the formula for the area of a rectangle is base times height.0564

The base is 20; the height is 10.0570

That is going to be 200 inches squared.0577

Then we have to find the area of this triangle because how much space is the triangle using up?0586

Because that is how much we have to take away.0595

The triangle, area is a base times height divided by 2; the base is 5.0598

Again even though this is not the bottom, that is not the base,0615

we can still call that the base as long as the base and the height are perpendicular.0620

5; and then the height is 6; over 2.0626

5 times 6 is 30; divided by 2 is 15; inches squared.0631

We have the area of the rectangle and the area of the triangle.0642

Let's take the area of a rectangle and subtract, take away0646

the area of the triangle to see what is left in blue.0651

It is going to be 200 inches squared minus 15 inches squared.0657

If you do 200 minus 15, you are going to get 185 left.0666

185 inches squared, this will be the area of the shaded region.0674

That is it for this lesson; thank you for watching Educator.com.0686