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(xA , yA), B(xB , yB) and C(xC , yC) 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:
formula for area of triangle given by vertices

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 dAB, dBC and dCD given by
dAB = √( (xA - xB)2 + (yA - yB)2)
dBC = √( (xB - xC)2 + (yB - yC)2)
dCD = √( (xC - xD)2 + (xC - yD)2)
The perimeter is given by
Perimeter =
dAB + dBC + dCD

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.

A ( , )
B ( , )
B ( , )


Area =
Perimeter =

More References and Links

Online Geometry Calculators and Solvers.