A Nice geometry math question| can you find the area?

Area of this quadrant, okay? Please, this is not drawn to scale. Now this is very easy, yes. But tactical, a bit, so let's call the center of this quadrant zero, let's call here zero. Let's call this point a. Let's call this point b. Okay, let's call this point c, and this meeting point. Let's call it b. All right, now the equation says we should find the area of the quadrant. and this length BC is equal to eight, and PB is equal to four. Now this quadrant, the area of a quadrant is one over four pi r squared, right? Okay, now first of all, let us find the radius of To get the radius, remember that a radius is any line drawn from the center of the circle. to any point on the circumference is the radius, so if I decide to draw this line from here to touch the center here, then to touch the circumference here, so it means that this is the radius, now let r be equal to the radius of the quadrant, okay, so that means This place is r now as well. Also note that ob is also r, because ob is also the radius. of this quadrant, so that simply means that if OB is equal to R, OP is equal to OB minus PB, so OP is equal to OB minus PB. Now, what is OB? OB is the radius of this circle. So you can see that OP is remembering that the radius is capital R minus PB is four, so we can replace OP with R minus four. At this point, let's look at triangle OCP. Triangle OCP, using the Pythagorean theorem using the Pythagorean theorem, if this is the first time you have seen us, please hit that subscription button and turn on the notification bell so that you don't miss our videos, all right? We upload our videos as often as possible. Give us a thumbs up if you're Actually enjoying these videos, so whenever you're convenient, always keep an eye out for our videos. There must be something new for you to watch, by God's grace. Okay, all right. So, using the Pythagorean theorem. This is what we have; here we have eight, here we have r, and this place is r minus four. So this is 90 degrees, so according to Pythagoras, r squared is equal to r minus four squared. plus eight squared; now remember that a squared minus b squared is equal to a squared minus 2ab plus b squared, okay, so that means that we can write this as r squared is equal to r squared minus 2 times r times 4 plus 4 squared, okay, then plus 8 squared so r squared equals r squared minus 2 times 4x r plus 4 squared is 16 plus 8 squared is 64 Now, if we continue, we can say r squared is equal to r squared minus 8r plus 16 plus 64 is 80 plus 80 so if we subtract r squared from both sides minus r squared minus r squared, so you can see that this and this will go right, so we are left with zero equal to 80 minus 8r. Okay, so let's Take this to the other side; if we do that, we have 8r equals 80, so let's divide both sides. divide both sides by 8, so we have 8r over 8 equal to 80 over 8; so 8 divided by 8 is 1, and we have that the radius is equal to 10, so that is the radius of the quadrant. Now the question says we should find the area of the quadrant; remember that the area of the quadrant is the area of the quadrant Is 1 over 4 pi r squared equal to 1 over 4 multiplied by pi multiplied by r squared? is equal to the area of the quadrant, okay, so we have 1 over 4 multiplied by pi multiplied by Our radius is 10. 10 squared is equal to what the area? So, 1 over 4 times pi times 10 squared is 100. is equal to a, excuse me, now wait for divine 200, we have 25, so we have 25 pi is equal to a Alright, so if you multiply this using your calculator, you can see. That pi multiplied by 25 is 78, so the area is approximately 78.54. square units. Okay, thank you so much for watching. See you in my next video.