For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Area of a Triangle

#### Related Links

- 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

### Basic Math Online Course

### 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 had*0472

*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 away*0646

*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

1 answer

Last reply by: Professor Pyo

Thu Jan 2, 2014 4:56 PM

Post by Magdy Mettias on December 22, 2013

thankyou mary you are such a great help

0 answers

Post by chin chang on May 16, 2012

Thanks,it really helped.