hi welcome to this quarter miles video in this video we're going to look at how to find the area of a quarter Circle so here we've been given a quarter Circle and we've been asked to find the area for this quarter Circle and to give our answer to two decimal places so as you can see we've got a radius another radius and a right angle so that's a quarter Circle and we've got the arc join in this and we're going to find the area of this quarter circle now a quarter circle is a quarter of a whole circle so if we had a whole circle like this our quarter Circle will be a quarter of it so if we find the area of the whole circle and then just divided by four we will find the area of the quarter Circle and just remember the area for circle area is equal to pi r squared so if we do the radius squared and multiply it by pi we'll get there the whole circle and then we can divide that by four to get there if the quarter Circle so let's get started so here we've got our quarter Circle so let's turn our quarter circle into a whole circle so let's just do a whole circle here Okay so we've got a whole circle and we've got our quarter Circle here in green and we've been asked to find there at this quarter Circle so let's find the area of the whole circle so if we have a look at our whole circle we've got a radius of 8 centimeters so to get the area of the whole circle we're going to do pi times 8 squared pi times the radius squared so let's do pi times eight squared on our calculator so pi times 8 squared and that's 64 Pi or 201.06 so on so we could write 64 Pi or we could write 201.06192 and so on and if you just put some dots you're showing that the number carries on but you just couldn't rebover to write it all out so we've got there of the whole so at 64 Pi or 201.06192 and so on centimeters per square now we want to find the area of the quarter Circle so we now just need to divide by four so we could do 64 pi divided by 4 or we could do 201.0619 and so on and then just press divided by four and that will give us if we divide by 4 that will give us another off over 16 Pi or 50.26548 and so on centimeters squared now we've been asking for answer to two decimal places so our answer is two decimal places will be 50.27 centimeters squared and that's there if this quarter Circle 50.27 centimeters squared so to find there for quarter Circle you find there the whole circle and then just divided by four okay let's have a look at our next question so next question is a non-calculator question and we've been given a quarter Circle and we've got a radius of six centimeters so if we have our whole circle the radius of the whole circle is six centimeters and we've been asked to find the area of the quarter Circle and to give our answer in terms of Pi so we know it's a non-circulated question so I'm just going to put my calculator down so let's find the area of the whole circle so that's going to be pi times the radius 6 squared so we'll do pi times 6 squared so 6 squared is 36 that's pi times 36 so that would be equal to 36 Pi centimeters squared so that's there of the whole circle but we want there if the quarter Circle so we now just need to divide by four so we're going to do 36 pi and then just divide by 4 and that will give us the area of the quarter circle now 36 divided by 4 is 9. so 36 pi divided by 4 would be 9 pi so answer is 9 pi centimeters squared so if this quarter circle is 9 pi centimeters squared and that's it okay let's have a look at our last question so last question says the area of this quarter circle is 30 centimeters squared and we've been asked to find Y which is the radius of the whole circle so there if this quarter Circle would be 30 centimeters squared now if we times that by 4 we'll find the area of the whole circle so if we do 30 multiply by 4 that's equal to 120 centimeters squared if we had a whole circle there if the whole circle would be 120 centimeters squared now we can use our formula pi r squared I know it's equal to 120 and then find out what Y is the radius of the circle so we'd have pi r squared so pi r squared now the radius of the circle is y so pi times y squared would be equal to 120. then normally remember whenever we find the area of the circle we Square the radius and then times it by pi so let's work backwards let's divide by pi so let's divide by pi and divide by pi and that will leave us on the left hand side we had pi times y squared if we divide that by pi we're just left with Y squared and then on the right hand side if we divide our 120 by pi 120 divided by pi that's equal to 38.19718 and so on in other words what we've done is we find the area of the whole circle is 120 Pi we notifying the area of the circle we Square the radius and times it by pi so we've divided by pi to find out what that would be now this is the radius squared y squared so we're going to square root to find out what the radius would be so we're going to do the y equals the square root of 38.19718 and so on and if we just do the square root of answering our calculator that gives us an answer of y equals 6.18 centimeters to two decimal places to two decimal places and that's it so if you're given the area of a quarter Circle if you times it by four you can find the area of the whole circle and then you can just work backwards by dividing by pi I'm working out the square root and then that will tell us our radius that's it and that's it so to find the area for quarter Circle you just find the area the whole circle and divided by four and that's it so I really hope you found this video useful thanks very much