 Hi and welcome to the session today. We will learn about area of triangle Suppose we are given a triangle a b c in which the coordinates of point a are x 1 y 1 coordinates of b on x 2 y 2 and coordinates of c are x 3 y 3 and We need to find area of triangle a b c then Area of triangle a b c is Given by half of the determinant Now the elements of determinant will be x 1 x 2 x 3 the x coordinates of these three points then y 1 y 2 y 3 the y coordinates of these three points and And the elements of say 3 will be 1 1 and 1 So in this way we can find out the area of the triangle given the coordinates of the three points of the triangle But to find out the area using determinants we need to remember few points so first point is since Area is a positive quantity We always take the absolute value of the Determinant point to be remembered is Area is given and we need to find out the coordinates of some point then use Both positive and negative values of The determinant for calculations Now if we have three colonial points Then there will be no triangle. That means area of triangle a b c will be equal to zero so The area of the triangle near points Zero let's take one example We need to find the area of triangle a b c where the coordinates of a r 2 7 coordinates of v r 1 1 and coordinates of c r 10 8 so area of Triangle a b c will be Half into the determinant and the determinant will be two one ten then seven one eight And one one one so this will be equal to half in two Two in two one into one minus eight into one here. We are expanding the determinant along r one Now minus seven into one into one minus ten into one Plus one into one into eight minus ten into one that is equal to One by two into 47 that is 23.5 so area of triangle a b c is 23.5 square units So in this session we have learned to find out area of triangle using determinant With this we finished this session. Hope you must have understood the concept. Goodbye. Take care and have a nice day