# Area of Triangle with Coordinates Calculator

Table of contents

Formula for area of triangle with verticesHow do you find the area of a triangle with coordinates?How do you calculate the perimeter of triangle using points?How to use this area of triangle with coordinates calculatorOther related calculatorsFAQsIf 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?

## Formula for area of triangle with vertices

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:

## How do you find the area of a triangle with coordinates?

To calculate the area of a triangle with its vertices *A(x _{1}, y_{1}), B(x_{2}, y_{2})*, and

*C(x*, follow these simple steps:

_{3}, y_{3})**Evaluate**the absolute value of the expression*|x*._{1}(y_{2}-y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2})|**Divide**this value by two to get the area of the triangle.- Verify this result using our area of a triangle with the coordinates calculator.

## How do you calculate the perimeter of triangle using points?

To calculate and find the perimeter of a triangle with its vertices *A(x _{1}, y_{1}), B(x_{2}, y_{2})*, and

*C(x*, follow these simple steps:

_{3}, y_{3})**Calculate**the length of the**side AB**using the**distance formula**

*AB = √[(x*._{2}− x_{1})^{2}+ (y_{2}− y_{1})^{2}]- Similarly,
**find**the lengths of the**sides BC**and**AC**using the**distance formula**. **Add**the lengths of the**three sides**to obtain the triangle ABC's perimeter.- Verify this result using our area of a triangle with the coordinates calculator.

## How to use this area of triangle with coordinates calculator

This calculator can do two functions simultaneously:

- Calculate the area of a triangle from 3 points.
- 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.

### How do you determine whether three points are collinear?

To determine whether any three points *A(x _{1}, y_{1}), B(x_{2}, y_{2})*, and

*C(x*are collinear, follow these steps:

_{3}, y_{3})**Evaluate**the value of the expression*|x*._{1}(y_{2}−y_{3}) + x_{2}(y_{3}−y_{1}) + x_{3}(y_{1}−y_{2})|- If this value
**equals zero**, the points are**collinear**. If this value is**non-zero**, the points are**non-collinear**.

### What is the area of the triangle formed by A(1,2), B(-1,1), and C(0,5)?

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

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