 Hi, this video is called Practice Problem 2. The instructions say to find the area of a regular pentagon with a potum length of 16 inches and to round to the nearest tenth. All right, when doing this problem, it's gonna be really important that you have your calculator handy. Things are gonna start getting a little tricky with your calculator with the whole idea of rounding. So I want your calculator close by so you can actually practice doing these calculations. Make sure you get the same thing that I do. If you just sit here watching the video and just trusting that my answers are right, you're losing out and you're missing out on really understanding this. So please be proactive when you watch this video and punch things in your calculator. Use your calculator, okay? So a pentagon, hopefully you can remember, a pentagon has five sides. So if you do your best to draw one, I won't judge you, I can't draw them very well myself. Something like that. You can go ahead and put dots at the vertices and mark all five sides as being congruent. You can clearly see mine don't look that way, but I did my best. Let's pick out our formula. Area of a regular pentagon will be one half perimeter times a potum. So all I need to do is figure out what my perimeter is and what my a potum is and I'll be set. And I'm lucky, they already gave me one thing that the a potum is 16. So all my work is concentrated on figuring out what that perimeter is. So let's think about this for a minute. The perimeter is the distance around my pentagon. If all five sides are the same, if I could just find one side length, I could multiply that by five and I would have my perimeter. So my goal really is to figure out what one side length is. Okay, so let's go ahead. When a perimeter has five sides, you can draw in five radii, which makes five triangles. That also means it's gonna have five central angles. So when you do 360 divided by five, that gets you to 72. We've seen that before. So all our central angles are 72 degrees. Now before I draw in the 72 on this last triangle, I can go ahead and drop down an a potum. I know that it's 16 long. And when I drop down that a potum, it bisected the segment. I don't know how long they are, but it also bisected the angle. 72 divided by two is 36. So it created a 36 and a 36. I think it is definitely time to take this little right triangle and draw it bigger so I can make sense of what's going on. That a potum was 16. This angle is 36, which would make this little guy be 54. And I'm gonna label this with X because that's what I care about because if I can find that, that's right here on the picture. So then if I double that, multiply it by two, I'll have my side length. Then if I multiply that by five, one, two, three, four, five, I'll have my perimeter, which is what belongs over here. So that is the goal. So we broke it down. Now it's time to put it back together. When I've got a right triangle like this, it's not a special right triangle because the angles aren't 45, 45, 90 or 30, 60, 90. So my only option is to use Sokotoa. I could either go from the 36 degree angle or the 54 degree angle. Let's go ahead and it really doesn't matter. Let's go from the 54. That makes the 16 the opposite and the X the adjacent. So tangent is going to be the appropriate choice. So I've got the tangent of 54 equals the opposite, which is 16 over the adjacent, which is X. Let's make that tangent of 54 into a fraction by putting it over one so we can cross multiply. So I end up with cross multiplying. 16 times one is 16. And then tangent of 54 times X, I could say X times the tangent of 54. Now be careful here. We're not going to multiply the tangent of 54 with the 16. Remember, my goal is to get the X alone and it's not alone yet. I've got to move that tangent of 54. So I divide both sides by the tangent of 54. And over here, the tangent of 54 is canceled. What do I get? Here's a chance I want you to pick up your calculator and practice punching it in. It's been a little while. 16 divided by the tangent of 54 gives you a big long decimal. That decimal is I got 11.62468045. Now this is where we're not allowed to round to the very end because it does stay round to the nearest 10th. I want the most exact answer I can find. And to get it as close as possible, I don't round till the end. So just leave your calculator alone. So this big long number is sitting on the screen of your calculator. Now let's take a second and remember what that is. So the sheet's about to get messy. Follow along, pay attention. This 11.624 equals X. Remember how X is the bottom part of this right triangle, which is the bottom part or one half of a side length of my pentagon. So let's think about this. If I, how many of those one halves do I have? How many 11.624s are there? Well, there's one right here and one right here. So there's two of them to make my side length. So that means there'll be two of them on this side of my pentagon, two of them over here, two of them over here, and two of them over here. So if I know that this little piece right here is that 11.624, that long number I have in my calculator, I'm going to hit times 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So I'm going to do that number times 10 in my calculator because that will give me my perimeter. So I've got it sitting in my calculator. I hit times 10. I get another big number. It tells me that that perimeter is 116.2468045. That is my perimeter. That's what goes into my formula, 1 1⁄2 perimeter times apathome. It's still too early to round. So hopefully you've left the 116.2468045 in your calculator. So all you have to do now is let's hit times 16. That gave me another big number. So I have 1⁄2 times 1859.948872. And the reality is that's not even necessary for you to write down. Just keep that in your calculator. And all you have left to do is multiply it by 1⁄2, which is the same thing as dividing by 2. And I got an answer. I'm out of room. I'll find some room. I got an answer that the area is 929.9744358. Now I am finally ready to round to the nearest 10th. So I look this 9. Does it stay at a 9 or does it round up? You look at the number after it. Since it's a 7, it's a 5 or bigger, this 9 would round up. And we actually would get 930.0 units squared as the answer to my problem. So looking back at that problem, that was a mess. Hopefully you were able to follow it. I'm sorry. My screen just kind of got a little bit small on me. And it is hard when you don't want to round till the very end. So I'm hoping you took good notes. You made them as clear as possible. And you will remember how to do a problem like this, where you can't round until the end.