 We can use the conservation property of areas to find the areas of some very, very complicated regions. So, for example, consider this type of figure, there's no good name for it, but we can still find the area provided that we know some measurements. So, here we'll assume our grid points are exactly one unit apart horizontally and vertically. And so, the way that we might begin is we might consider, well, how would we form this figure from a large rectangle? So, we might take a large rectangle and start cutting out the pieces that we don't want or need in the figure. So, we might start by getting rid of this piece here, and then maybe do a cut along here, and then maybe do a few more cuts, maybe I'll get rid of this, and a square there, another chunk there, there, and there. And after I've cut all these pieces out, I have my figure. So, how do we find the area of the figure? Well, we'll start with the area of the large rectangle. And then, because we removed pieces, we'll just subtract the areas as we go along. So, first thing we'll figure out is the area of this large rectangle that's six squares along each row. And there's four rows, the total area that's going to be 24 square units. And we'll start cutting out the pieces that we're not going to keep. So, let's see, well, this was our first removed part. So, we got rid of that part to begin with, and we want to figure out how big that is. Now, that's actually a triangle, and the thing to remember about any triangle is that its area is going to be half of the rectangular box that includes it. So, the triangle that we wanted is going to be half the area of that box. And so, that area is going to be total by area, the box is going to be six, the area of the triangle is going to be three, and we're getting rid of it. And so, my area so far running total 24 minus three. Now, the next part that we removed this is also, again, a triangular shape. And a triangle, again, has half the area of the box that encloses it. This box has area one, two square units. So, the triangle itself has area one, getting rid of it, reduces our area by one. Well, let's cut out this big portion here, that square there, that has area one, two, three, four, get rid of it, that's gone. We have another triangle here, half the area of the enclosing box, area of that triangle is going to be one, that's gone. Another triangle, also area one, another triangle area, half the enclosing box, one, two, three, four. The enclosing box has area four, so this triangle has area two, we'll get rid of it. And likewise, this triangle also has area two, get rid of it. So, I've started with my big rectangle, got rid of a couple of triangles, a square, a few more triangles, and a few more triangles. And what's left is the area of the figure, which works out to be ten square units.