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Video: Area of Triangles

Kathryn Kingham

Learn how to calculate the area of a triangle using the formula: area = half of base times height. Starting with rectangles and parallelograms and then cutting them in half, we talk through the process with some examples and emphasize that units of area are squared.

07:33

Video Transcript

Let’s talk about finding the area of a triangle. And I guess before we talk about finding the area of a triangle we need to talk about what the area is. Area is really simply a size of a surface. So here you can see I just coloured in the surface of this triangle, and we want to figure out how big it is. So let’s dive in.

Okay, I know what you’re thinking, “These aren’t triangles!” But before we figure out how to find the area of triangles, I want us to take a step back and try and remember how do we find the area of a parallelogram. So we can find the area of a parallelogram here, a square here, or a rectangle. But, if you remember, when we find the area of a rectangle, we take the length and we multiply it by the width. Another way to write that, sometimes we say the base and we multiply it by the height. Either way, we got length and width, base and height, doesn’t matter. We take these two numbers and we multiply the base times the height to find the area. But now what I want us to do is I want us to cut these guys in half, okay? We’re gonna cut our parallelograms, our quadrilaterals, in half. And what you should start to see is that every one of these is made up of two triangles, two equal triangles. How does this matter? Why does this matter? We’re gonna find out. So remember, we said the area of this square would be base times the height. But our goal here is to find out the area of a triangle. Well the thing is this triangle is half of the square, so the formula for finding the area of a triangle is by taking half of what the quadrilateral’s area would be: base times height divided by two is the simple way we say it. So we say base times height and divide it by two. Let’s try it.

Okay, here’s our first example. So someone has already told us the base and the height, the height and the base of this triangle. So what we need to start with then is our formula, which we remember is area equals the base times the height divided by two. All we need to do is figure out that the base is eight and the height is four. We can plug that into our formula by saying eight times four divided by two, okay? Eight times four divided by two. Eight times four is thirty-two, and then we divide thirty-two by two for a final answer of sixteen. So before we move on, I wanna tell you something really important about the area. Our answer is not just sixteen; our answer is sixteen centimeters squared. Any time we’re dealing with area, it’s so important that you know what it is that you’re working with. What are we measuring our triangle in? And this time, we’re measuring our triangle in centimeters, so we wanna make sure that we include our centimeters squared.

Okay example two, this time again we’ve been given all of our measurements: we’ve been given three, four, and five. So what I want you to be careful of when you’re trying to solve the area of triangles is knowing what is the height and what is the ba-what is the base. So here is the key to finding the height and the base. You first need to look for the right angle, okay? So your height and your base will always be connected to the right angle portion. So if we go back to our last example problem, it looked like this, right? But remember, we had this symbol. We had a little symbol right here that told us, “Oh! height and base.” When we’re dealing with a right triangle, it’s the same. We have this right angle which tells us, “Okay here’s our base, and here’s our height.” And the thing is, right now we do not even need this five meters. We don’t need that five meters to figure out anything about the area, so we can ignore that guy and we can move on and say three meters times four meters divided by two is gonna give us the area of this triangle. So we say three times four is twelve, divided by two. And again, that’s six but we do not forget these meters. We bring our meters down, and it’s meters squared. We deal with area; we deal with our units, squared.

Example three is for you. So what I want to do to you right now is just stop what you’re doing, pause. Pause the video, and write this down and see if you can find the area of this triangle. Go ahead pause it; I’ll wait. The answer is thirty feet squared. So I hope you got that and you were successful. But if you didn’t get the whole problem, then don’t worry I’m gonna walk you through this one again. So area, first we write our formula area equals one-half times the height times the base. We figure out that the right angle tells us which one is the height and which one is the base. So we have a ten-foot base, and we have a six-foot height. You need to divide that by two. six times ten is sixty, divided by two is thirty. And again, we say this is area; we can’t forget our units, thirty feet squared.

Now you’re ready to go out and solve all the triangle area problems. Just remember these two key things: one, that your formula is area equals height times the base divided by two and, number two, always add the unit squared at the end. You’ll be good to go. Happy area finding!