Area of Triangle with Coordinates Calculator

If you wish to calculate a triangle area with vertices, then this area of a triangle with coordinates calculator is the right tool for you! You can also use this calculator to find the perimeter of the triangle with vertices. In this article, you shall learn:

• What is the formula for the area of a triangle with vertices?
• How do you find the area of a triangle with coordinates?
• How do you calculate the perimeter of triangle using points?
• How do you determine whether three given points are collinear?

The formula for the area of a triangle from its three vertices is given by:

where:

• $\text{Area}$ is the area of the triangle $ABC$;
• $(x_1,y_1)$ are the coordinates of the vertex $A$;
• $(x_2,y_2)$ are the coordinates of the vertex $B$; and
• $(x_3,y_3)$ are the coordinates of the vertex $C$;

This simple formula is handy for calculating the area of a triangle given 3 coordinates. Another way to express this same formula is by using a determinant. To calculate the triangle area from 3 points:

To calculate the area of a triangle with its vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), follow these simple steps:

1. Evaluate the absolute value of the expression |x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|.
2. Divide this value by two to get the area of the triangle.
3. Verify this result using our area of a triangle with the coordinates calculator.

To calculate and find the perimeter of a triangle with its vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), follow these simple steps:

1. Calculate the length of the side AB using the distance formula AB = √(x₂ − x₁)² + (y₂ − y₁)².
2. Similarly, find the lengths of the sides BC and AC using the distance formula.
3. Add the lengths of the three sides to obtain the triangle ABC's perimeter.
4. Verify this result using our area of a triangle with the coordinates calculator.

This calculator can do two functions simultaneously:

1. Calculate the area of a triangle from 3 points.
2. Calculate (or find) the perimeter of a triangle with points.

Simply enter the coordinates of the triangle vertices, and this calculator will do the rest.

We have more triangle calculators for you:

• Triangle area calculator;
• Similar triangles calculator;
• 3 sides triangle area calculator;
• Square feet of a triangle calculator;
• Scalene triangle area calculator;
• Area of an obtuse triangle calculator;
• Area of oblique triangle calculator; and
• Area of a triangle SAS calculator.

To determine whether any three points A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃) are collinear, follow these steps:

1. Evaluate the value of the expression |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|.
2. If this value equals zero, the points are collinear. If this value is non-zero, the points are non-collinear.

3.5 units. To calculate this value yourself, follow these steps:

1. Evaluate the absolute value of the expression |(1)×(1−5)+(−1)×(5−2)+(0)×(2−1)| = |−4−3+0| = 7.
2. Divide this value by 2 to get 7/2 = 3.5.
3. Verify this result using our area of a triangle with the coordinates calculator.