Introduction to Irregular Polygon Area Calculator:
Irregular polygon area calculator is an online tool that helps you to find the area of an irregular polygon. Our tool is used to evaluate the area of the polygon that does not have equal sides and angles from the given function.
The area calculator polygon irregular is a helpful tool for students, teachers, and professionals as it gives solutions to the area of irregular polygon questions in a few seconds without any error in the calculation process.
What is the Area of an Irregular Polygon?
The area of an irregular polygon is the measurement of the volume that is enclosed in a polygon whose side and angle are unequal or have irregular shapes. It is called a non-regular polygon.
It is a useful method that is used in various fields like in geographic information systems to calculate the land areas, and boundaries in architecture and engineering used to design irregular building models and in computer graphics used for graphical simulations, calculating areas of complex shapes.
Formula for the Area of an Irregular Polygon:
The area of an irregular polygon formula consists of the area of a triangle and the area of a rectangle. The formula behind the irregular polygon area calculator is used to find the areas of the nth-term.
$$ A \;=\; \frac{1}{2} \biggr| \sum_{i=1}^{n-1}(x_i y_{i+1}) + (x_n y_1 - y_n x_1) \biggr| $$
Here, (xi,yi) are the coordinates of the vertices, and n is the number of vertices.
How to Find the Area of an Irregular Polygon?
To find the area of an irregular polygon can have the serval methods, depending on the complexity of the shape. In the process of finding the area of an irregular polygon, you need the coordinates of the polygon's vertices of a plane. Here is the stepwise calculation of the area of an irregular polygon.
Step 1:
Identify the coordinates of the vertices in sequence, either clockwise or counterclockwise.
Step 2:
Apply the formula of the irregular polygon according to the shape of the irregular polygon.
$$ A \;=\; \frac{1}{2} \biggr| \sum_{i=1}^{n-1}(x_i y_{i+1}) + (x_n y_1 - y_n x_1) \biggr| $$
Step 3:
Put the coordinates vertices value in the above formula and simplify it to get the solution of an irregular polygon.
Solved Example of the Area of an Irregular Polygon:
The irregular polygon area calculator helps you determine the area of irregular polygon easily but its important to understand the step-by-step calculation process. So, an example is given below,
Example:
Find the area of the irregular polygon (1,1),(4,1),(6,4),(4,6),(1,4)
Solution:
The given coordinates point (xn,yn) for the given irregular polygon,
$$ (1,1),\; (4,1),\; (6,4),\; (4,6),\; (1,4),\; (1,1) $$
The formula of the area of an irregular polygon,
$$ A \;=\; \frac{1}{2} \biggr| \sum_{i=1}^{n-1}(x_i y_{i+1}) + (x_n y_1 - y_n x_1) \biggr| $$
Put the given vertices coordinates point in the above formula and calculate the sum,
$$ \sum_{i=1}^{n-1} (x_i y_{i+1}) + (x_n y_1) $$
$$ 1 . 1 + 4 . 4 + 6 . 6 + 4. 4 + 1 . 1 $$
$$ 1 + 16 + 36 + 16 + 1 \;=\; 70 $$
Calculate the sum yi xi+1
$$ \sum_{i=1}^{n-1}(y_i x_{i+1}) + (y_n x_1) $$
$$ 1 . 4 + 1 . 6 + 4 .4 + 6 . 1 + 4 . 1 $$
$$ 4 + 6 + 16 + 6 + 4 \;=\; 36 $$
Subtract both the sum of y_ix_i+1 and x_i+1y_i,
$$ 70 - 36 \;=\; 34 $$
Put these values in the area of the irregular polygon formula,
$$ A \;=\; \frac{1}{2} \times 34 \;=\; 17 $$
Therefore the irregular polygon area is 17sq units.
How to Use the Area of an Irregular Polygon Calculator?
Area of irregular polygon calculator is an easy-to-use tool, so you can use it to evaluate the area of the given irregular polygon.
Before adding the input for the solution of given irregular polygon area problems in the irregular polygon area calculator, you must follow some simple steps. These steps are:
- Enter the coordinate vertex value that you want to evaluate through the formula of the irregular polygon in the input field.
- Recheck your input value for the solution of the area of the irregular polygon question before hitting the calculate button to start the calculation process.
- Click on the “Calculate” button to get the desired result of your given irregular polygon area problem.
- If you want to try out the area of a 5 sided irregular polygon calculator to check its accuracy in solution, then you can use the load example.
- Click on the “Recalculate” button to get a new page for solving more irregular polygon area questions.
Final Result from Area of 5 Sided Irregular Polygon Calculator:
Area of irregular polygon calculator gives you the solution to a given area of irregular polygon problem when you add the input value to it such as:
- Result Option:
Click on the result option for a solution of irregular polygon area questions.
- Possible Step:
When you click on the possible steps option it provides you with the solution of the area irregular polygon problem in steps.
Advantages of the Area of an Irregular Polygon Calculator:
Area calculator polygon irregular gives you many advantages whenever you use it to calculate irregular polygon area problems and to get its solution. These advantages are:
- Our area of 5 sided irregular polygon calculator saves the time and effort that you consume in solving area of regular polygon questions and get solutions in a few seconds.
- It is a free-of-cost tool that provides you with a solution for a given Irregular polygon problem to find the area without paying a single penny.
- The area of irregular polygon calculator is an adaptive tool that allows you to find the area of irregular polygon problem.
- You can use this area calculator of irregular polygon for practice to get familiar with this concept easily.
- It is a trustworthy tool that provides you with accurate solutions as per your input to calculate the area of irregular polygon problems.
- The irregular polygon area calculator is limitless so you can use it multiple times for calculation of the area of irregular polygon.
