To find the area using coordinates, you can follow a step-by-step process. First, ensure that the polygon you are working with is not crossed.
Then, number the vertices of the polygon in order. Next, create a table with the x and y coordinates of each vertex.
Multiply the x coordinates of each vertex by the y coordinates of the vertex in the row below and subtract the product of the y coordinates of each vertex multiplied by the x coordinates of the vertex in the row above. Repeat this process for each consecutive pair of rows and add the results together.
Finally, divide the final result by two and make it positive if necessary. Online calculators are available that use the Jarvis march algorithm to build a convex hull and automatically perform these calculations for rectangles or quadrilaterals.
Key Points:
- Make sure the polygon is not crossed
- Number the vertices of the polygon in order
- Create a table with the x and y coordinates of each vertex
- Calculate the difference between the products of x and y coordinates for each consecutive pair of rows
- Add the results together
- Divide the final result by two and make it positive if necessary
1. Use An Online Calculator To Find The Area Of A Rectangle Or Quadrilateral Using Coordinates
Finding the area of a rectangle or quadrilateral using coordinates can be a complex task, but thanks to online calculators, the process has become much simpler. These calculators eliminate the need for manual calculations and provide a quick and efficient way to determine the area based on the given coordinates.
To get started, all you need to do is input the coordinates of the vertices of the shape, and the calculator will do the rest.
2. Calculator Uses Jarvis March Algorithm To Build A Convex Hull
One of the key algorithms used by online calculators to determine the area of a rectangle or quadrilateral is the Jarvis march algorithm, also known as the gift wrapping algorithm. This algorithm helps in building a convex hull, which is a polygon that encloses all the given points.
The convex hull is essential in calculating the area of the shape accurately.
3. Calculate Four Sides Of The Hull And One Diagonal Between First And Third Points
Once the convex hull is constructed, the calculator proceeds to calculate the four sides of the hull. Each side is determined by the coordinates of its endpoints.
Additionally, the calculator also calculates the diagonal between the first and third points, as it is required for further calculations. These measurements are crucial for accurately determining the area of the rectangle or quadrilateral.
Calculating the area of a quadrilateral:
5. Number Vertices Of Polygon In Order, Either Clockwise Or Counter-Clockwise
To ensure accurate calculation of the area, it is important to number the vertices of the polygon in a specific order. This order can be either clockwise or counter-clockwise, as long as it remains consistent throughout the process.
Numbering the vertices provides a clear definition of the shape and its orientation, which is crucial for subsequent calculations.
6. Use X And Y Coordinates Of Each Vertex To Calculate Area
To calculate the area of the rectangle or quadrilateral, we need to utilize the X and Y coordinates of each vertex. By considering these coordinates, we can determine the lengths of the sides of the shape and perform calculations using geometric formulas.
7. Create Table With X And Y Coordinates Of Each Vertex
To organize the information, it is helpful to create a table that lists the X and Y coordinates of each vertex. This table acts as a reference tool, making it easier to visualize and perform calculations accurately.
By listing the coordinates systematically, you can eliminate potential errors and ensure a smooth calculation process.
8. Multiply First Row (X) By Second Row (Y) And Second Row (X) By First Row (Y)
To calculate the area using the coordinates, we utilize a simple mathematical operation. First, we multiply the values in the first row (X) of the table by the corresponding values in the second row (Y).
Then, we multiply the values in the second row (X) by the corresponding values in the first row (Y). Finally, we subtract the second product from the first.
This process is repeated for each consecutive pair of rows, and the results are added together.
By dividing the final result by two and considering the sign, we obtain the area of the rectangle or quadrilateral defined by the given coordinates. However, it is important to note that this method may not work for crossed polygons, as their area calculation requires different techniques.
By utilizing online calculators that implement these steps and formulas, users can easily and accurately find the area of rectangles and quadrilaterals using coordinates. These tools provide a convenient solution for a task that would otherwise require intricate calculations and a deep understanding of geometric principles.
So, the next time you need to find the area of a shape using coordinates, remember to take advantage of these helpful online resources.
Summary:
– Use an online calculator to find the area of a rectangle or quadrilateral using coordinates
– Calculator uses Jarvis march algorithm to build a convex hull
– Calculate four sides of the hull and one diagonal between first and third points
– Divide quadrilateral into two triangles and calculate area of each using Heron formula
– Number vertices of polygon in order, either clockwise or counter-clockwise
– Use x and y coordinates of each vertex to calculate area
– Create table with x and y coordinates of each vertex
– Multiply first row (x) by second row (y) and second row (x) by first row (y)
– Subtract second product from first
– Repeat for each consecutive pair of rows and add results together
– Divide final result by two and make positive if necessary
– Method does not work on crossed polygons
– Provides an area calculator for users to try with their own coordinates
Tips:
1. Plot the coordinates on a graph before calculating the area to visually understand the shape you’re working with.
2. If the shape is a rectangle, you can simply multiply the length by the width to find the area, without needing to use complex formulas or algorithms.
3. If the shape is a regular polygon (e.g., square, equilateral triangle), you can use a simplified formula specific to that shape to find the area more efficiently.
4. If the coordinates of the vertices are not given, but you have the equation of the sides of the shape, substitute specific values for x or y to find the coordinates of the vertices.
5. Remember to use the correct units when providing the coordinates and reporting the area to ensure accurate calculations and clear communication.
