 A circle with radius 12 cm has a segment with a central angle of 90 degrees. What is the area of the segment? We have a circle over here and this shaded region bounded by the chord PQ and this arc of the circle makes up a segment and we need to figure out its area. So how do we go about this? So in our circle we have a sector POQ which makes a right angle at O, the center of the circle. This is my sector POQ. Now as you can see this sector is made up of a triangle POQ and this segment over here. So if I subtract the area of this triangle, if I remove this triangle from my sector, what I'll be left with is the area of my segment. I'll be left with this blue region and this is the area that we need to figure out. So let me just clearly write it out for you. The area of our triangle POQ subtracted from the area of our sector POQ will give us the area of our segment. So why don't you go ahead and figure out the individual areas of this sector and triangle and do it on your own. So the area of any sector is pi r squared which is area of a circle times the angle it makes at the center of the circle divided by the total angle in a circle which is 360 degrees and area of a triangle is half into its base into its height and if we subtract triangles area from our sector's area, we'll get the area of our segment. So here we have pi r squared r is given to us as 12 centimeters. So pi r squared is pi times 12 times 12, theta is 90 degrees. So theta by 360 is 90 degrees by 360 degrees. Let's simplify this. So 90 by 360 is 1 by 4. So an interesting thing to note here is that area of a sector which makes an angle of 90 degrees at the center is one fourth of the total area of the circle and sectors such as this are known as quadrants of a circle. Now moving on to our triangle POQ, if OP is the base, OQ would be the height of our triangle and vice versa and as we can see OP and OQ both are radii of our circle. So their lengths would be 12 centimeters each. So this means the area of our triangle is 1 by 2 times 12 times 12. Now let's simplify this to find the area of our segment. So 2 times 6 is 12, 6 times 12 is 72, so triangles area is 72 centimeters square and here 4 times 3 is 12, 12 times 3 is 36, times pi is 36 pi. So area of our sector is 36 pi centimeters squares. So we can say the area of our segment over here is 36 pi minus 72 centimeters square.