 In the previous video, we found the area of this regular pentagon with a side length of 6 by finding the area of 5 separate triangles. Will that rule work for every regular polygon? So, in a sense, we found the area as the number of side lengths, in this case 5 times 1 half base times height. Now, in these triangles, we had a height, which was found with trigonometry, and then the base length referred to one of the side lengths of the pentagon. So, all of these lengths were 6 units long. And so, this base unit, let me just rewrite that as 5 times 1 half times a side length of the pentagon times the height. Now, this height, the red segment that we've just drawn, when we're dealing with regular pentagons, that height is also called the apathome. Please note that that apathome is different from these blue segments, which are called radii. Radii connect center point to vertices, apathome connects center point to the midpoint of one of the side lengths. So, I'm going to rewrite this. I had 5 times 1 half times a side length times the height of the triangle, which we call the apathome. And now, this works for a pentagon, but what about if I had, let's say, a hexagon, or a septagon, or an octagon? The only thing that would change is this number. That number refers to the number of sides. So, in general, the area of a regular polygon is number of sides times half times the side length times the apathome. Now, we can simplify this a little bit more because multiplication is commutative. You can simplify this to, let's say, 1 half times n times s times a. And now, n times s. In this pentagon, there are 5 sides, and all of those sides are 6 units. So, the perimeter is the number of sides times that side length. In general, the perimeter of any regular polygon is the number of sides times how long one of those side lengths actually is. And so, we can substitute this value into our formula and have an area formula as 1 half times apathome times the perimeter of the polygon.