Polygon Area and Perimeter calculator with points

Polygon Area and Perimeter calculator with points

Polygon Area and Perimeter Calculator

Number of Vertices Displayed Decimal Digits
Vertex X Value Y Value
1
2
3
4
5
6
7
8
9
10
Perimeter   
Area  

To calculate the area and the perimeter, begin at the top of the left column and number each point, starting at 1, proceeding to the right column . Enter the number of vertices in the form, then enter each vertex's x and y values. After entering the required data, click the Calculate button to obtain the area and the perimeter. As written, the calculator can process up to 10 vertices.

After clicking the Calculate button, the coordinate values, area and perimeter will displayed using the specified number of decimal digits. The coordinate values displayed are those used to calculate the area and perimeter, so changing the displayed decimal digits may change the x and y coordinate values and may result in the calculation of different values for the polygon's area and perimeter. For many practical problems of interest, results calculated and displayed using 3 decimal digits are adequate.

Clicking the Reset button will erase the form's content and set the number of vertices and displayed decimal digits to 3.

How do you find the perimeter and the area with points?

x- and y-coordinate determine the position of a point right from and above the origin in the cartesian coordinate system. Edge lengths and perimeter have the same unit, the area has this unit squared.

To find the distance between two points, find the change in x and y and use them as a and b in the Pythagorean theorem: √[a² + b²]. To find a shape's perimeter, add up all the distances between its corners.

The area is then given by the formula:

  n
A = Σ| xi * yi+1 - yi * xi+1 | / 2
 i=1

Formulas to find the perimeter and the area with points

Length of edge i = √ ( xi+1 - xi )² + ( yi+1 - yi

  n
p = Σ ( xi+1 - xi )² + ( yi+1 - yi
 i=1

  n
A = Σ| xi * yi+1 - yi * xi+1 | / 2
 i=1

with xn+1 → x1 and yn+1 → y1