Area of a Triangle

Area of a Triangle in Coordinate Geometry:

Using Coordinates:

  • Given Points: Three vertices of a triangle with coordinates (x1,y1), (x2,y2), and (x3,y3).
  • Formula: The area of the triangle formed by these points is given by the formula: Area=12x1(y2y3)+x2(y3y1)+x3(y1y2)

Steps to Find Area:

  1. Identify Coordinates:

    • Points A, B, and C with coordinates A(x1,y1), B(x2,y2), and C(x3,y3).
  2. Apply Area Formula: Area=12x1(y2y3)+x2(y3y1)+x3(y1y2)

  3. Perform Calculations: Substitute the values of coordinates into the formula and solve the expression.


Given the coordinates of vertices A(1, 3), B(4, 6), and C(7, 1), find the area of the triangle ABC.

Steps to Solve:

  1. Identify Coordinates:

    • A(1,3), B(4,6), and C(7,1).
  2. Apply Area Formula: Area=121(61)+4(13)+7(36)

  3. Perform Calculations: Area=12589 Area=1212 Area=122 Area=6 square units


The area of the triangle formed by the points A(1, 3), B(4, 6), and C(7, 1) in the coordinate plane is 6 square units. This area formula based on coordinates allows for the calculation of a triangle's area without using the lengths of its sides, relying solely on the coordinates of its vertices.