 This video is called Practice Problem 3. The instructions say to find the area of a regular triangle with a side length of 12 inches round to the nearest 10th. Well, there's actually a few ways we could, excuse me, there's a few ways we could go about solving this problem. I'm going to show you the introduction to both ways and then I'm going to pick the one that I think is easier to take all the way through, all right? To find the area of a regular triangle, where a regular triangle is just another name for equilateral. So regular side length of 12 inches means it's an equilateral triangle where all the sides then are 12. So we could certainly use the formula that we've been working on today where we have area equals one-half perimeter times apothem. It's really easy to see that the perimeter would be 36 because 12 plus 12 plus 12 is 36. And then we could go ahead and start taking the routine that we're used to to find the apothem. Or if you go in the center of your triangle, a triangle has three sides, so it will have three radii. When you do 360 divide by 3, you get all of these to be 120. When you drop down that apothem, it bisects the side length into 6 and 6 and it bisects the 120 to 60 and 60. So we've created a right triangle where I've got this side to be 6, the apothem is what I'm looking for. This is 60, which would make it a 30, 60, 90. So then I would know that opposite the 30 is my n, opposite the 60 is my n-rat 3, and opposite the 90 is my 2n. I'm going to stop this method right here. At this step, what you would need to do is solve for this. When you do that, well, maybe I won't stop. Let's just go ahead and do it. You would get 6 equals n-rat 3. So you would divide both sides by root 3. Over here, they cancel. So you have n equals 6 over the square root of 3. To put this in proper form, we would have 6-rat 3 over 3, which equals 2-rat 3. So I would get my n to be 2-rat 3. And so if n is 2-rat 3, I actually just found my apothem because opposite the 30 was my apothem and opposite the 30 is n. Since n is 2-rat 3, I could go ahead and plug that in. So then to finish, I'd multiply these numbers together. 1 half times 36 is 18. Then you'd have 18 times 2-rat 3, which give you 36-rat 3 units squared for your area. This problem does say to round your answer to the nearest 10th. I personally like 36-rat 3 as my answer. It's more exact, but if we are going to round in your calculator, you'll do 36 times the square root of 3. And that rounds to, or it is a 62.353, which will round up to 62.4 units squared. So technically, that would be the right answer for this problem. Now, that way works great, but I promised you two methods. I didn't give myself a ton of room. We'll see if I can fit it into this little box right here to show you the second method. Maybe some of you already thought of it. This formula, area equals 1 half per meter times a pothem, is totally fine to use. We got the right answer, but you know another formula for finding area of an equilateral triangle. And that is, that other formula you learned for area of an equilateral or regular triangle is side length squared root 3 over 4. Well, we were told at the very beginning that the side length was 12, so go ahead and plug that into your formula. So when the side length's 12, it becomes 12 squared root 3 over 4, so that would simplify 12 squared is 144 root 3 over 4, and 144 divided by 4 becomes 36. So we landed on the same answer of 36 root 3 unit squared, which is the same thing I got in my other problem, so that would round again to 62.4 units squared. So a nice thing is when you're dealing with an equilateral triangle, you have options. If you like 1 half per meter times a pothem, use it. If you like side squared root 3 over 4, use it. For an equilateral triangle, personally, I prefer side length squared root 3 over 4 simply because it was faster, less steps, less chance to goof up, but it is your option. Use what works best for you.