 Our job is to find the area of a regular pentagon with a side length of six. First of all, remind yourself what it means for a polygon to be regular. All of the sides are congruent, so that means all of these sides are all six units long, and all of the interior angles are congruent as well. Angle P is congruent to angle A, T, N, and E. Now our task is to find the area of the entire yellow shape. In order to do that, we'll split up the shape into five congruent triangles. Each of the blue segments that I just drew, they're all radii of this circle, and as a result, all of those radii will be congruent, since radii from one circle will all be the same length. So I have isosceles triangles, and they all have the same base, which is six, so I have five congruent triangles. Let's just investigate one of those triangles. So in that triangle, we're given that this base length is six, and furthermore, well, to find the area of one triangle, we want to use area as half base times height, and we're already given one base length, which is six, but we do need to find the height. In order to find the height, we're going to have to use a little bit of trigonometry. Let's go back to the original pentagon, and look at that point G. It's gotten covered up a little bit, but that point G is the center of the pentagon, and from G, there are five angles that are created. There's one angle, two, three, four, and five angles, and all of the angles together make 360 degrees. So if I just want to find one of the angles, I can call that a central angle is 360 divided by five, which in this case is 72 degrees. However, that 72 degrees refers to this entire angle, and I don't need to use that entire angle. Instead, I'll just use half of that central angle. So this angle, let's say, is 36 degrees, because 36 is half of 72. Now, we're just looking at this triangle, which is a right triangle, and we know that the angle up top here is 36 degrees. Our goal is to find this length, which would be an adjacent leg, because we're dealing with right triangles. And then, since the original blue triangle was isosceles, with a base length of six, I know that half of a side length will be three units long, because that altitude splits up the base into two congruent parts. So now to find the height of the triangle, which we labeled as x, we'll use the tangent function. Tangent of 36 degrees is equal to the opposite over adjacent, which is the unknown x. So that means that x is equal to three divided by the tangent of 36 degrees. In this case, x is roughly equal to 4.129. Now that number, 4.129, refers to this length in the triangle, which corresponds with this height of the blue triangle. In other words, we've now found that length in the pentagon. So one of the original blue triangles we can now say is area is one half times the base, which we saw was six, times the height of the triangle, which we found to be 4.129. But remember, there are five separate triangles. Here's one of them, two, three, four, and five. So we'll multiply this entire thing by five, and we eventually get an area of 61.937.