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How to Find the Area of a Triangle With Coordinates

If you are studying geometry, whether you are young or old, an important area of study is the ability to calculate the area of geometric shapes, including triangles. When given the coordinates of three vertices of a triangle on a coordinate plane, you can use this simple formula to solve for the area of the triangle.

Instructions

    • 1

      Multiply the value of each X-coordinate by the difference between the other Y-coordinates. For point A, you will need to calculate the value of Ax multiplied by (By -- Cy). For point B, you will need to calculate the value of Bx multiplied by (Cy -- Ay). For point C, you will need to calculate the value of Cx multiplied by (Ay -- By). For each of these calculations, Ax and Ay are the x and y coordinates of point A, Bx and By are the x and y coordinates of point B and Cx and Cy are the x and y coordinates of point C.

    • 2

      Add these three values together. Do not be concerned if the total of these three values is a negative number.

    • 3

      Divide this total by 2. The absolute value of this total is the area of the triangle, which will always be a positive number.

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