A Nice geometry math question| solve for area of the rectangle

Hello, wonderful friends, welcome back to my channel. Please, this is not drawn to scale. The question states that we should find the area of this particular rectangle, which is the area of ABC. Now this is the radius of the large circle and three is the radius of the smaller circle. and in the middle of this large circle, because this is not drawn to scale; this is supposed to touch This is at some point, so this is at the center of this larger circle, which is also at the center of this. Line, okay, all right. Now, the area of a rectangle is what? Length times breadth. Length times breadth. so it means that if we can find the length of AB and multiply it by the length of AD Then we are done. Now, first of all, let us try to find the length of AB. The length of AB. Let's analyze first, remembering that any line drawn from the center of the circle to the circumference Is a radius okay? So, if I draw this line from the center of the circle to the circumference? Let's call this radius eight, right? So this is also eight. All right, and this place is Equal to this place, okay? So if I call this t, then t is also equal to eight, right? So we have eight here. Now we have found parts of line AB. Similarly, from here to here is also three, which is the radius. of the smaller circle, so it means that if I call this point P, then PB is also equal to three. Okay, so this place is three. We have found from here to here, which is eight, and from here to here. which is three, the only thing that remains is TP, so how do we find it? First of all, let us Draw a line because this line is perpendicular to this line. Right, sorry, this line is parallel. parallel to this line and perpendicular to line AB, so we have this right; so if I should drop a parallel line to TP. Okay, now we can decide to drop a straight line to join the two centers of These two circles, okay, so let me join that. All right, now remember that this is also 90 degrees. okay, and from here to here is the radius of the larger circle, which is eight, and from here to here is the radius of the smaller circle, which is three, so it means that this length is eight plus Which is 11 now coming to this side? Remember that this place is also parallel to this place. so it means that from here to here is three, right? But the whole of this is eight, so if this place is three, then from here to here is what eight minus three, which is five. Now let us draw out. Please click the subscription button and turn on the notification bell if this is your first time You're seeing us, okay? Give us a thumbs up if you're actually enjoying this video, and please Always say that you're confident there must be something new for you to watch by God's grace. Thank you very much. So let's go ahead and draw the right angle we formed. This is not drawn to scale. Scale, please. Now, this place is what eight plus three, which is 11. From here to here is unknown. but from here to here is five, okay? Now let's call this x. Using the Pythagorean theorem. Using the Pythagorean theorem, then we have that 11 squared is equal to 5 squared. plus x squared, so let's move this to the other side: 11 squared minus 5 squared equals x. Remember that a squared minus b squared equals a minus b multiplied by a plus b. so we can write this as 11 minus 5 multiplied by 11 plus 5 is equal to x squared. Now 11 minus 5 Six, so we have 6. 11 plus 5 is 16, so we have 16 equal to x squared. Now, 6 times 6 is 36, right? 6 carried 3, 6 times 1 is 6, plus 3 is 9, so we have 96 equals x squared, which simply means that x is the square root of 96, which is equal to. Now I don't want to leave my answer in radical form. So I want to write it in decimal form; let's use the calculator from this phone, okay? so we have the square root of 96, which is approximately approximately 9.8, okay, 9.8 units—that is the length of TP, okay? So TP is 9.8 units. All right, so in essence, the the length of this particular rectangle is equal to All right, now AB is equal to 8 plus 9.8 plus 3. Okay. All right, now we have AB is equal to 8 plus 3 is 11, and 11 plus 9.8 is 20.8. Okay, so we have found AB. Now what remains is AD. Now remember what I said—that this is not drawn to scale—but the center of this circle coincides with the center of the arc, so if the center of this circle aligns with the center of AD Now remember that from here to here is also the radius of this circle, which is 8. so it means that from here to here is also 8, and from here to here is also 8, so it simply means That advertisement is 8 times 2, or 8 plus 8, which equals 16; therefore, the area of rectangle ABCD is equal to ab multiplied by ad, so this is equal to 20.8 multiplied by Ad 16, so let's go ahead and write that: 20.8 multiplied by 16, which is equal to 332.8. Great job, I hope you enjoyed this video. Thank you so much for watching. See you in my next video. Goodbye