Perimeter and Area of a Triangle Given its Vertices

Online calculator to calculate the area and perimeter of a triangle given the coordinates of its vertices. The distance formula is used to find the distances between vertices then these distances are used to find the perimeter and area of the triangle.

Formulas for Area and Perimeter

Let A(x_{A} , y_{A}), B(x_{B} , y_{B}) and C(x_{C} , y_{C}) be the three vertices defining the triangle. The formula for the area of the triangle
defined by the three vertices A, B and C is given by:

where det is the determinant of the three by three matrix.
The perimeter is found by first finding the three distances beteween the three vertices d_{AB}, d_{BC} and d_{CD} given by
d_{AB} = √( (x_{A} - x_{B})^{2} + (y_{A} - y_{B})^{2}) d_{BC} = √( (x_{B} - x_{C})^{2} + (y_{B} - y_{C})^{2}) d_{CD} = √( (x_{C} - x_{D})^{2} + (x_{C} - y_{D})^{2})
The perimeter is given by
Perimeter =d_{AB} + d_{BC} + d_{CD}

How to use the calculator?

Enter the x and y coordinates of the three vertices A, B and C of the triangle and press "calculate". The outputs are the area and perimeter of the triangle.