If you’re reading this, you’ve likely come across a polygon with given coordinates and are seeking to find its area. Luckily, by using the coordinates, you can find the area of a polygon accurately and quickly.
In this guide, I will walk you through the step-by-step process of finding the area of any polygon using coordinates. If you also wonder how to use coordinates to find the perimeter of polygons, I wrote a whole article that I encourage you to read.
Step 1: Plot the Points
Start by plotting the points of the polygon on a coordinate plane. Make sure to label each point with a letter for later reference when finding the distance between each point.
Step 2: Connect the Points
After plotting each point of your polygon, connect each of the points in the order they are given to form the sides of the polygon, giving you a visual representation of the shape.
Step 3: Divide into Triangles
Then, divide the polygon into triangles by drawing lines from one vertex to all other vertices except for the two adjacent. This will divide the polygon into triangles and make it easier to calculate the area.
Step 4: Find the Base and Height
For each triangle, find the base and height. The base is the distance between two vertices, and the height is the perpendicular distance from the third vertex to the base.
Step 5: Calculate the Area of Each Triangle
Using the base and height, calculate the area of each triangle using the formula: Area = 1/2(Base x Height).
Note: Suppose it is not a square or rectangle. In that case, I suggest you subdivide the polygon into smaller sections containing rectangles, squares, triangles, and other shapes with easily calculable areas. Then add those areas together.
Step 6: Sum Up the Areas
To find the area of the polygon, sum up the areas of all individual triangles (or other figures) calculated in step 5.
Alternative Methods: Using Determinant
To find the area of a polygon, you need to use the determinant. The formula to find the area of a polygon is:
A = (1/2)[Det(x1,x2,y1,y2)+Det(x2,x3,y2,y3)+ … +Det(xn,x1,yn,y1)],
where Det(a,b,c,d) = ad-bc.
Where (x1, y1), (x2, y2), …, (xn, yn) are the vertices of the polygon.
Watch the video below to learn more about how to use determinants to find the area of a polygon.
You can also use online calculators to find the area of a polygon using coordinates. You need to input the coordinates of the vertices, and the calculator will give you the area of the polygon. With this method, you don’t need to worry about the formula.
What to read next:
- Understanding Angle Bisectors: Everything You Must Know!
- Here’s How To Factor Polynomials (5 methods with examples)
- Gradients and Areas Under Graphs: Definitions, differences, and Applications!
Wrapping Up
Finding the area of a polygon using coordinates is a simple process that can be achieved by following the steps I outlined in this article.
Remember to label each point, connect them to form the sides, divide the polygon into triangles, find the base and height, calculate the areas of each triangle, and then sum everything up.