00:01
So in this problem, we are dealing with a square that initially has sides of length 16 inches.
00:08
And we are essentially going to be drawing lines from all of the sides of the midpoints of the square in order to form a new square in the middle.
00:17
And then we are going to be shading two of the triangles on the outside region here and adding up the area.
00:25
And then once we do that, we are going to be creating another square from our new midpoints.
00:31
And adding the area there.
00:33
So we can see that this is going to end up being a geometric series.
00:37
So our first area of our small triangles, since we know that these two legs were formed from the midpoints, we know that each triangle is going to have an area of one half times our base, which is eight, times our height, which is eight.
00:51
And since we have two of these, we can just multiply this by two.
00:54
And so the area of our two outside red triangles is going to be 64 square inches.
00:59
And then we also know that this, leg right here is going to have a length of 8 times a square to 2.
01:07
That's just from our properties of right triangles...