 This video is called find the area of the shaded region 2. Well to find the area of the shaded region it makes sense for you to find the area of the entire shape. In this case it's a triangle and think of the triangles being pink with a cutout. So you have a big piece of paper in the shape of a triangle and we cut out what looks like a square maybe it's a rectangle. So it would make sense to find the area of the shaded is to take the area of the entire shape and subtract out the cutout, the area of the rectangle. So we will do the area of the triangle minus the area of the square of the rectangle. We'll put them together and see if we have any like terms that we can combine. So let's start with the big shape finding the area of the triangle. To find area of a triangle its base times height divide by two or one half base times height. So I'll have one half times 4x times 6x. Well 4x times 6x is 24x squared and one half times 24x squared is the same thing as 24x squared divide by two which gives me 12x squared. So the area of the triangle is 12x squared. Next let's find the area of the rectangle or the square. We'll have to do for rectangular square is base times height. So I'll have to do base which is x plus 3 times the height which is x minus 2. Since we're multiplying binomials I'll have to foil first outside inside last. So x times x is x squared. X times negative 2 is a negative 2x plus 3x minus 6. I have like terms to combine x squared plus 1x minus 6. So I'll put that in for the area of my square. So now I have to actually subtract the 2. I'm going to have to distribute. This negative really is a negative 1 so I'll apply it to everything. So I'll take my 12x squared and rewrite it exactly as is. And then I'll have a negative x squared minus x and negative 1 times negative 6 is a positive 6. I can see that I have a couple like terms to combine. I have a 12x squared minus 1x squared which gives me 11x squared. And then I have a minus 6 minus x plus 6. That will represent the area of the shaded region. Because I took the area of the entire shape which was the triangle which gave me an area of 12x squared. I subtracted out the area of the rectangle which was this and ended up with 11x squared minus x plus 6.