This irregular shape is hiding something/geometry challenge

Let's solve for the value of x. Don't mind we are asked to find the area of this shape. Welcome back to my channel. First things first, looking at this I think let's name this A, B, C and D. So to find the area of this irregular shape or this compound shape, we are going to join, let's join B to D first so that we get a particular shape that we know. For now we don't know the shape that we have here. So let's get the particular shape that we know. And we have a triangle, at least we know this one. Okay, so because this is a triangle, let's find area of triangle A, B, D. Okay, so I've got that to attend to myself. So looking at this, we have area of a triangle is half base times height. Therefore, area of triangle A, B, D is half multiplied by, the base is for 11, while the height is 60. So if we solve this two, we're going to 60, 30 times, right? Now we have 11 multiplied by 30. That is area. So area of the triangle is equal to, if you're multiplying a number by 11, just add the two numbers. 3 plus 0 is 3. We add it at the center to get 330. So this is 330 square meters. So it means that the area of this place is 330 square meters. Now, if this is the first time you are coming across this channel, please hit the subscription button and turn on your notification bell so that you don't miss our videos. We upload our videos as often as possible. Do tune in at your convenience. There must be something new for you to watch. Give us a thumbs up. I'm just trying to be sure this is still on. Give us a thumbs up if you love what we are doing and always comment. Yes, I'm always in the comment section. Tell me whatever you want in the comment section and I'll be there to respond. Okay, thank you. Now that we have found this, we need area of this place in order to solve for the full area of the shape. Now, first of all, area of this, for us to get it is not easy because this is not a right angle triangle and we don't know this length, length BD. But we can actually solve for BD using this, using ABD, right? Because BD, because triangle ABD is a right angle triangle, it means that line BD is the hypotenuse. And using the Pythagorean theorem, BD squared will be equal to AB squared plus AD squared. Now, BD squared is equal to AB squared, that is 60 squared, this one, plus AD squared, 11 squared. So, BD squared is 3,600 plus 1, 2, 1. So, I would like you to watch to the end because I'm going to learn a lot besides what we are just doing. I'll be introducing some math tricks and I will explain them along the way, okay? So, 3,600 plus 121 will give us 3,721. Now, our BD will be square root of 3,721. And to solve this, I can do this without my calculator. So, let me introduce this math trick for you and I'm going to also leave it as one of the end screens at the end of this video so that you go to the particular videos and watch all the math tricks, okay? Now, looking at this, we first of all look at the last number here. The last number here is 1. So, we shrink from number 1 to number 9. The two numbers that they are square, we end with 1. The two numbers are 1 and 9 because 1 squared is 1 and 9 squared is 81. Both of them end with 1. So, what this is telling me is that the square root of 3,721, we end with either 1 or 9, okay? So, I will now write 1 or 9. Then, what do I do next? I'll cancel this and now concentrate on 37, okay? So, now 37, I look for a number that when I square it, I will get a number that is exactly 37 or less than 37. And that number is 6 because 6 squared is 36. If I choose 7, 7 squared is 49 and you can see 49 is definitely bigger than this. So, it's only 6 that will fit in. That means our answer is either 61 or 69. So, let me write it here, 61 or 69. Now, how do we know the particular one that is the answer? Note, this works when the number you are working on is a perfect square, okay? When the number you are working on is a perfect square, that is when this trick will work. So, now we have 61 and 69. How do we know the one that is going to work? First of all, after 6, we have 7, right? After 6, you count 7 and 6 times 7 is 42. Now, we are going to compare this 42. I don't know if you can see that because sometimes my camera cuts that side off. So, what I basically did is after 6, I will count 7. I said 7 times 6 is 42. So, I'm going to compare this 42 with this 37 now. So, you can see that 37 is less than 42. Therefore, I'm going to pick the lesser number. So, it simply means that the square root of 3,721 is 61. I hope that is clear. If it's not clear, like I said, I'll be leaving the playlist of my math trick as end screen to this video. So, after watching this, you can go and watch as many as you want. This is also part of the math trick in my playlist. So, it means that square root of 3,721 is 61. Therefore, BD is 61. Now, to find the area of the triangle, because the triangle is an escalating triangle, all the sides are unequal, we can do this using the Heron's method, right? Using the Heron's formula, the area is square root of s brackets s minus a, s minus b, s minus c. And our s is the perimeter of this triangle divided by 2. So, it's going to be 61 plus 40 plus 55, everything divided by 2. Now, if we solve this 61 plus 40 is 101 plus 55 is 156. So, we have 156 divided by 2, which will give us 100 divided by 2 is 50, 50 divided by 2 is 25, 6 divided by 2 is 3. So, if we add this, we have 50 plus 25, 75 plus 3 is 78. So, we have 78 as our s. Have you subscribed yet? If you have not, please do that. So, it simply means that the area now is going to be the square root of 78 brackets, 78 minus, let's take this side as our a, 61. 78 minus, for b, let's take here, 55. Then bracket 78 minus, for c, let's take 40. So, area then will be the square root of 78 brackets. 78 minus 61 will give us 17. 78 minus 55 will give us 23. 78 minus 40 will give us 38. So, if we solve this, I'm going to do that using a calculator. So, our a will be equal to the square root of, so let's solve this, 78 multiplied by 17 multiplied by 23 multiplied by 38. We have 1,158,924. Now, if we should find the square root of this, square root of 1,158,924, we are going to have the area to be 1,076.5 to one decimal place. Thank you so much and see you in my next video. Bye. Oh, sorry. This area is going to be in That is for this only. Okay. We have not actually found the whole area. So, the area of the whole shape now will be this plus this. I forgot. And if we do that, we are going to have 1,406.5 square meters. And that's our final answer. If you actually watch to the end, simply means that you are my true subscriber and I'm so happy that you watched the end. So, to know that you actually watched the end, just give me two thumbs up in the comment section. Two thumbs up in the comment section. Okay. With that, you are going to receive a special hug. Thank you so much for watching and see you in my next video. Bye.