00:02
Okay, so for this problem, you're given an octagon or a diagram of an octagon in which you can see the apatham is labeled to be two feet long, and you're asked to find the area of the octagon, and if necessary, run into the nearest tenth.
00:22
So our first step in solving this will be to find the central angle of this polygon.
00:30
So we know that the central angle of any polygon is equal to 360 degrees divided by the number of sides that it has.
00:42
An arrow up here that it's given that n is equal to 8 because it's an octagon has eight sides.
00:48
So 360 degrees divided by 8 is equal to 45 degrees.
01:05
So given this information, if we, for instance, if we had the center point of this polygon, and we had two adjacent vertices, we know that the line between these two vertices is going to be equal to s.
01:29
And we know that if you drew a line from each vertex to the center point, you would create the central angle right here.
01:40
But the information that they give us is about the apatham.
01:44
So if we drop an apatham down the middle of this triangle, bisecting the central angle, we actually create two right angle, two right triangles next to each other, in which both of these triangles, which let me just, i'll just make it bigger.
02:14
Easier to see.
02:16
So we can see this is one of the triangles, that this angle right here is going to be equal to half of the central angle because the apathem had bisected it.
02:29
And we know that this length right here is going to be equal to the apatham, and that this length right here is going to be equal to one half of the side length.
02:39
So let's solve for this new angle.
02:41
This new angle, which i'll call theta, and it's going to be equal to 45...