 Let us learn to calculate the area of a segment of a circle. Now what is a segment? When you draw a chord of a circle such as AB, you get two kinds of segments. One is a minor segment shown in green and other is the major segment shown in orange. How do we calculate the area of these segments though? First of all let us consider this as a center of the circle. And if this center is O, we will join OA and OB. And then the area of minor segment which we can read as AXBA can be given by area of the sector OAXB minus area of triangle OAB. Now in order to find the area of the segment AXBA, we must know some information since we need to know the area of the sector OAXB. It is expected that we will know this angle theta at the center so that we will be able to calculate the area of the sector and length of the chord L so that we can find the area of the triangle. In some cases we might be provided with the area of the triangle OAB directly. Now let us say this R is 10 centimeters. And if L is 10 root 3 and the center angle is 120 degrees. What is the area of the segment AXBA? Now this area of the segment AXBA is in green. So we will use the green color. So area of segment AXBA is equal to area of the sector is theta which is the center angle subtended by this particular sector divided by 360 degrees times pi times R square minus area of triangle OAB. Now I want to calculate the area of triangle OAB first. Since we have this space here, this is how we are able to approximate the triangle. Let's say this is the height of the triangle and we already know the base of the triangle and the perpendicular drop from the center each of these parts will be 5 root 3. This will be 10 and how we can find out H by Pythagoras theorem and so we have H square is equal to hypotenuse square minus 5 root 3 square. This gives me H square to be equal to 100 minus 75 equal to 25 and therefore H is equal to 5 centimeter. And from here we can find the area of the triangle OAB as half times base of the triangle which is 10 root 3 times the height which is 5 and this gives us 25 root 3 square centimeter. Let us quickly write this value for the area of the triangle OAB that is 25 root 3 square centimeter and now let us proceed with finding out the area of the sector. Area of the given sector will be equal to 120 degrees divided by 360 degrees times pi times R square which is 100. This gives us 100 by 3 pi square centimeter and let's put this value here and so we can simplify this by putting the value of pi and root 3 we get the area of the segment AXBA as 61.418 square centimeter and this is how we can calculate the area of the given segment of the circle.