 For this next problem, we're given a regular hexagon. We're also given that the hexagon's perimeter is 60 units. And it's our job to find the area of this regular hexagon. Using the formula that we derived earlier with the pentagon, we can say area is 1 half apathome times perimeter. And in that formula, we already know the perimeter, but we do need to find the apathome. Now remember, the apathome of a regular polygon is from the center point to the midpoint of one of the opposite sides. In order to find the length of the apathome, let's split up the regular polygon into triangles. So we have six green triangles, and if we just consider one of them, let's look at this one. The known information from the fact that the perimeter is 60 units, that means each of these side lengths will be 10 units long. And so likewise, our side lengths are 10. Our job is to find the length of the apathome. In order to find the length of the apathome, let's first figure out some angle measurements. One central angle in a regular hexagon, so central angle will be 360 divided by the number of angles that there were, in this case divided by 6. So that gives us a central angle of 60 degrees. However, when we split up those central angles with the apathome, we're splitting up into two congruent angles. So if both of those angles that I just drew in this one and that one, both of those angles add up to 60, that means one of them is 30 degrees. 30. And so our goal is to find the apathome length. Now let's just consider half of one of these triangles. That triangle we know has a 30-degree angle, a 90-degree angle, and our job is to find that length. So in other words, we have a 30-60-90. Now remember, 30-60-90s will happen with a hexagon, not necessarily with other polygons. So always check your work. Now we need to find one more side length. The fact that the entire side length of a side in the pentagon, or in the hexagon is 10, means that half of a side length will be 5 units apiece. So now we have the side length of our 30-60-90. And remember, the short leg is N, 2N, and N root 3. So that apathome length, that apathome is going to be 5 root 3. So now we have enough information we can solve for the area of our regular hexagon. Area is 1 half times apathome times perimeter. And remember, because multiplication is commutative, that's the same as saying 1 half times 5 times 60 times root 3. And half of 5 times 60 is just 300. No, it's not. Half of 5 times 60, I know 5 times 60 is 300, and half of that should be 150 times root 3, square units.