How to Calculate the Area of Any Polygon Using Drawing Methods
In Google maps, a polygon is an object drawn on the google map to represent an area surrounded by a closed path (or loop). The polygons are similar to polyline objects in that they consist of a series of coordinates in an ordered sequence. Polygons are drawn with a stroke and fill. You can define custom colours, weight, and opacities for the edge of the polygon (the stroke) and similarly for the enclosed area (the fill).
Area Polygon Drawing can best describe the complex shapes including:
The intersection of one or more than one area.
Areas with holes in them.
A single polygon defines different noninfected areas.
It is feasible to use a polygon with multiple paths to define a complex shape.
Read the article below to know the steps to draw a polygon in Google Map.
How to Draw a Polygon on Google Map?
You can draw a polygon in a Google map to show the area you are interested in. To draw, zoom in, or zoom out of the map as you need to best include the area of your interest. Select Add polygon from the toolbar at the top of the map. A new dialogue box will appear. As the dialogue box will appear on the screen, you will find 5 tabs with 5 different tasks.
The first tab is Description, where you can describe your area or include any image or link associated with it. The second tab is colour, where you can change the width, colour, and opacity of the lines you are drawing. The third tab is the View tab, which will show you the latitude and the longitude of the area you have drawn by clicking on the Snapshot Current View button in the right corner of the screen. The fifth tab is the Measurement Tab, which will give you the exact perimeter and area of a polygon.
How to Draw a Polygon in Google Earth?
Following are the steps to draw a polygon in Google Earth:
Click on Add Polygon (CTRL + Shift + G), from the toolbar at the top.
The new polygon dialogue box will appear on the screen, and the cursor changes to a square drawing tool. Enter the properties of your drawing just as you would do for any other type of data. This properties tab enables you to change the name and style colour for the polygon from the default white to better visualize the shape you are looking for.
Draw a Polygon: Click on the map to start drawing a polygon using the following freehold method.
Free - Form Shape - Click once and drag. The cursor changes to an up-arrow to represent that you are using free-form mode. The outline of the shape follows the path of your cursor, as you drag the cursor around the 3-D viewer. If you are constructing a polygon, a shape expands from the path of your cursor, always joining the beginning and ending points.
Regular Shape - Just click and release. Move the mouse to the new point and click to include additional points.
You can adjust the dimension of the polygon by using the Measurement Tab. The measurement will appear in a dialogue box as you draw. You can also view measurements for your shape with the help of the Drawing Tool.
You can even edit your saved drawing by selecting the Drawing from the Places Dialog box, clicking the left mouse button and select properties.
How to Make a Polygon in Google Earth?
Following are the steps on how to make a polygon in Google Earth:
A polygon is a two - dimensional shape in Google Earth. The polygon icon looks like this (Image will be uploaded soon).
Click on Polygon Icon - You can see a familiar dialogue box appears on the screen as shown below.
Similar to the path and placement tab, you can add a description and title, and observe some additional information about the polygon shape here. One of the best things that can be done is that you can change the colour and width of the border, and the colour and opacity of the fill.
To make a polygon, simply start left clicking around the polygon. Click on the left mouse button to add points and the right mouse button to remove points.
Fill colour in a 'Style colour Tab' and ‘Change the Line’ - You can change many properties of a polygon including the opacity.
You can even give it a 3D look to the polygon by clicking on the Altitude Tab, and then changing the mode to 'relative', and putting a value. The option 'Extend Sides To Ground' will change the polygon from the floating plain to a box of sorts.
FAQs on Area of Polygon by Drawing: Step-by-Step Guide
1. What is the fundamental concept behind finding the area of a polygon by drawing?
The fundamental concept is to decompose or divide the complex polygon into a set of simpler, non-overlapping shapes for which we have standard area formulas. Typically, these shapes are triangles, but can also include rectangles and trapeziums. By calculating the area of each simple shape and then summing them up, you can find the total area of the original polygon.
2. How do you find the area of an irregular polygon using the triangulation method?
The triangulation method involves these steps:
Draw the polygon: First, accurately draw the irregular polygon on paper or a grid.
Pick a vertex: Choose any single vertex of the polygon.
Form triangles: From the chosen vertex, draw straight lines (diagonals) to all other non-adjacent vertices. This will divide the entire polygon into a series of triangles.
Calculate individual areas: Find the area of each triangle using the formula Area = ½ × base × height. You will need to measure the base and the corresponding perpendicular height for each triangle.
Sum the areas: Add the areas of all the triangles together to get the total area of the irregular polygon.
3. Can you give a step-by-step example of finding the area of an irregular pentagon by drawing?
Certainly. To find the area of an irregular pentagon ABCDE:
First, draw the pentagon.
From a single vertex, say A, draw diagonals to the non-adjacent vertices C and D.
This action divides the pentagon into three distinct triangles: ΔABC, ΔACD, and ΔADE.
Next, calculate the area of each triangle separately by measuring its base and perpendicular height.
The total area of the pentagon is the sum of the areas of these three triangles: Area(ABCDE) = Area(ΔABC) + Area(ΔACD) + Area(ΔADE).
4. Why is dividing a complex polygon into simpler shapes a reliable method for finding its area?
This method is reliable because area is an additive property. This means the total area of a larger shape is exactly equal to the sum of the areas of its smaller, non-overlapping parts. Since we have proven and universally accepted formulas for simple shapes like triangles and rectangles, breaking down a complex polygon into these basic components allows us to use these reliable formulas to build up an accurate measurement of the total area, no matter how irregular the polygon's shape is.
5. What is the main difference between calculating the area of a regular polygon and an irregular polygon?
The main difference lies in the formulaic approach. A regular polygon has equal sides and equal interior angles, which allows us to use a single, direct formula to find its area, such as Area = ½ × apothem × perimeter. In contrast, an irregular polygon has sides and angles of different measures, so there is no single direct formula. It must be divided into simpler shapes (like triangles or trapeziums), and the total area is found by summing the areas of these individual parts.
6. How is the concept of finding a polygon's area used in real-world scenarios?
This mathematical concept has several practical applications:
Land Surveying: Surveyors use this method to calculate the precise area of irregular plots of land for property valuation and development.
Architecture and Construction: Architects and engineers calculate the floor area of rooms or the surface area of structures with non-standard shapes.
Computer Graphics: In digital design and video games, algorithms use polygon decomposition to calculate the area of a shape to be filled with colour or texture.
Agriculture: Farmers might use it to estimate the area of a field to determine the amount of seed or fertiliser needed.
7. What are the most common mistakes to avoid when calculating a polygon's area by decomposition?
The most common mistakes include:
Incorrect Height Measurement: Using a slanted side instead of the perpendicular height when calculating the area of a triangle.
Overlapping Shapes: Drawing diagonals or lines in a way that the smaller shapes overlap, which leads to counting a portion of the area more than once.
Arithmetic Errors: Simple mistakes made when adding the individual areas of the triangles or trapeziums.
Forgetting Formulas: Forgetting to divide by two in the triangle area formula (½ × b × h) is a very frequent error.
8. How can you find the area of a polygon if its vertices are given as coordinates on a graph?
When the vertices of a polygon are given as coordinates (e.g., (x₁, y₁), (x₂, y₂), etc.), you can use a powerful method called the Shoelace Formula (or Surveyor's Formula). This algebraic method eliminates the need for drawing and measuring. It involves listing the coordinates in order, performing a series of cross-multiplications, and summing the results to find the exact area without dividing the shape into triangles manually.
