Alright, so now we're going to learn how to calculate the area of a triangle on the graph. We're going to do this a few different ways in this class, but the formula stays the same. You might remember this: Area of a triangle equals half times base times height. We usually just write this as half bh. Right? That's the same thing. Half bh. So, that is our area of a triangle formula. Let's go ahead and use it on the graph a few different ways.

So here on graph A, what I want to do is pick this point right here, and I want to calculate the area below the blue line but above that point. Alright? So that sounds a little crazy, but let's go ahead and visualize it on the graph. It's going to be above or below the blue line and above that point. So what we would have is a line here connecting this to the point, and now you can kinda see what triangle I might be talking about. I'll highlight it here in yellow. Alright. So there's going to be a few times in this class that we'll use a graph like this to calculate this area.

Alright, so how do we do it? First, we have to define what's going to be our base and what's going to be our height, and then we have to find out what those are, right? So here, we're going to have our base be this part right here, the dotted line, and our height is going to be coming up right here. That's going to be our height. So let's figure that out. For our base, it looks like we started here at 0 for the x-values, right? 0 down here and we went all the way to 3, right? From 0 to 3, so our base is 3. It looks like we started at 3 and went up to 6. So our height is 3. We are ready to do our formula. Area equals 12×3×3 which simplifies to 4.5.

We are going to do a fractions review, a decimal review, all this stuff. If any of this math is tripping you up, we have reviews for all of it.

Let's go ahead and do example B here. We've got that same point there where they're intersecting, but now I want to go ahead and find the area below this dotted line. So, again, I'll highlight it in yellow here, the area I'm talking about. So this area, highlighted in yellow, this triangle, how do we figure out what the area is? So again, we're going to use our same formula, half base times height, so we need to know what our base is and what our height is. Here we've got a base along this dotted line. The base is from 0 to 4, so it's 4 units. The height is from 1 to 4, giving us a height of 3. So, Area equals 12×4×3 and equals 6.

One more example here, example C. In this situation, I want to find the area of this triangle right here. So, they could give us this point right here. They could tell us that the x value is 2 and we need to find the area in between this point. So, though it seems a little trickier, it is almost the same. We've got to find the height. So, looking at this triangle sideways, we see we've got the height right here along the middle. That's the height of that triangle and our base is this whole long line right here in green. So, base equals 6 and height equals 2. Now that we know our base and our height, let's calculate our area. Area equals 12×6×2 which comes out to 6 again.

That's three different ways that we're going to use this formula in this class to calculate areas of triangles.

Let's move on.