This online calculator helps to calculate, determine and calculate the area of a land plot online. The presented program is able to correctly suggest how to calculate the area of land plots of irregular shape.
Important! The important area should fit approximately into the circle. Otherwise, the calculations will not be entirely accurate.
We indicate all the data in meters
A B, D A, C D, B C- The size of each side of the plot.
According to the data entered, our program online to perform the calculation and determine the area of land in square meters, ares, acres and hectares.
Method for determining the size of the site manually
To correctly calculate the area of plots, you do not need to use complex tools. We take wooden pegs or metal rods and place them in the corners of our site. Next, using a measuring tape, we determine the width and length of the plot. As a rule, it is sufficient to measure one width and one length, for rectangular or equilateral sections. For example, we got the following data: width - 20 meters and length - 40 meters.
Next, we move on to calculating the area of the plot. With the correct shape of the site, you can use the geometric formula for determining the area (S) of a rectangle. According to this formula, you need to multiply the width (20) by the length (40), that is, the product of the lengths of the two sides. In our case, S = 800 m².
After we have determined our area, we can determine the number of acres on the land plot. According to generally accepted data, one hundred square meters - 100 m². Further, using simple arithmetic, we will divide our parameter S by 100. The finished result will be equal to the size of the plot in hundred parts. For our example, this result is 8. Thus, we get that the area of the site is eight acres.
In the case when the area of the land is very large, then it is best to carry out all measurements in other units - in hectares. According to generally accepted units of measurement - 1 hectare = 100 acres. For example, if our land plot, according to the measurements obtained, is 10,000 m², then in this case its area is equal to 1 hectare or 100 acres.
If your plot is of an irregular shape, then in this case the number of acres directly depends on the area. For this reason, using the online calculator, you can correctly calculate the parameter S of the plot, and after that dividing the result by 100. Thus, you will receive calculations in hundreds. This method makes it possible to measure plots of complex shapes, which is very convenient.
Total information
The calculation of the area of land plots is based on classical calculations, which are performed according to generally accepted geodetic formulas.
In total, several methods are available for calculating the area of land - mechanical (calculated according to the plan using measuring palettes), graphic (determined by the project) and analytical (using the area formula according to the measured boundary lines).
To date, the most accurate way is deservedly considered - analytical. Using this method, errors in calculations, as a rule, appear due to errors in the terrain of the measured lines. This method is also quite complicated if the boundaries are curved or the number of angles on the plot is more than ten.
The graphical method is a bit simpler in terms of calculations. It is best used when the boundaries of the plot are presented as a broken line, with a few turns.
And the most accessible and simple method, and the most popular, but at the same time the biggest error is the mechanical method. Using this method, you can easily and quickly perform the calculation of the land area of a simple or complex shape.
Among the serious shortcomings of the mechanical or graphic method, the following is distinguished, in addition to errors in measuring the area, in the calculations an error is added due to paper deformation or an error in drawing up plans.
Programming environment:
Visual Studio 2013
In this example, a polygon is built by the number of sides n, coordinates of the center of the polygon and distance R from the center of the polygon to its side. All this data is entered by the user and starts to be processed by pressing the "Build" button. The program allows you to draw polygons with different parameters on one shape.
Function button1_Click receives input parameters and processes them for correctness. In the case of incorrect data: a negative number of sides or a negative distance, the program informs about incorrect data (if negative coordinates are entered, the polygon is displaced relative to the field of view and, at certain values, may be completely out of the field of view (out of the form), as in the case of entering a sufficiently large value distance). If the data entered by the user is correct, then control passes to the function lineAngle, which directly constructs the polygon.
Program code:
using System; using System.Collections.Generic; using System.ComponentModel; using System.Data; using System.Drawing; using System.Linq; using System.Text; using System.Threading.Tasks; using System.Windows.Forms; namespace pravilnyy_mnogougolnik (public partial class Form1: Form (public Form1 () (InitializeComponent ();) int n; // number of sides int R; // distance from center to side Point Cntr; // center Point p; // array of points of the future polygon // create an array of points for our polygon private void lineAngle (double angle) (double z = 0; int i = 0; while (i< n+ 1 ) { p[ i] . X = Cntr. X + (int ) ( Math. Round (Math. Cos (z/ 180 * Math. PI ) * R) ) ; p[ i] . Y = Cntr. Y - (int ) ( Math. Round (Math. Sin (z/ 180 * Math. PI ) * R) ) ; z= z+ angle; i++; } } private void button1_Click(object sender, EventArgs e) { label10. Text = "" ; // get input data and check for correctness n = Convert. ToInt32 (textBox4. Text); R = Convert. ToInt32 (textBox5. Text); Cntr. X = Convert. ToInt32 (textBox6. Text); Cntr. Y = Convert. ToInt32 (textBox7. Text); if (n< 0 || R < 0 ) label10. Text = "Invalid input!"; else // input data is correct, draw a polygon(p = new Point [n + 1]; lineAngle ((double) (360.0 / (double) n)); int i = n; Graphics g = pictureBox2. CreateGraphics (); while (i> 0) (g. DrawLine ( new Pen (Color. Black, 2), p [i], p [i - 1]); i = i - 1; ))) // keep the drawn polygon, zero out the inputs for the new input private void button2_Click (object sender, EventArgs e) (textBox4. Text = "0"; textBox5. Text = "0"; textBox6. Text = "0"; textBox7. Text = "0"; label10. Text = ""; ) // erase everything drawn without zeroing out the last input private void button3_Click (object sender, EventArgs e) (pictureBox2. Image = null; label10. Text = "";)))
Distance and Length Units Converter Area Units Converter Join © 2011-2017 Mikhail Dovzhik Copying of materials is prohibited. In the online calculator, you can use values in the same units! If you are having difficulty converting units of measurement, use the Distance and Length Unit Converter and Area Unit Converter. Additional features of the calculator for calculating the area of a quadrilateral
- You can navigate between input fields by pressing the right and left keys on the keyboard.
Theory. Area of a quadrilateral A quadrilateral is a geometric figure consisting of four points (vertices), no three of which lie on one straight line, and four segments (sides) connecting these points in pairs. A quadrilateral is called convex if the segment connecting any two points of this quadrilateral will be inside it.
How do you know the area of a polygon?
The formula for determining the area is determined by taking each edge of the polygon AB, and calculating the area of the triangle ABO with the vertex at the origin O, through the coordinates of the vertices. When walking around a polygon, triangles are formed that include the inside of the polygon and are located outside of it. The difference between the sum of these areas is the area of the polygon itself.
Therefore, the formula is called the surveyor's formula, since the "cartographer" is at the origin; if it walks counterclockwise, the area is added if it is to the left and subtracted if it is to the right in terms of the origin. The area formula is valid for any self-non-intersecting (simple) polygon, which can be convex or concave. Content
- 1 Definition
- 2 Examples
- 3 A more complex example
- 4 Explanation of name
- 5 Cf.
Polygon area
Attention
This could be:
- triangle;
- quadrangle;
- pentagon or hexagon and so on.
Such a figure will certainly be characterized by two positions:
- Adjacent sides do not belong to the same straight line.
- Nonadjacent ones have no common points, that is, they do not intersect.
To understand which vertices are adjacent, you need to see if they belong to the same side. If yes, then the neighboring ones. Otherwise, they can be connected by a segment, which must be called a diagonal. They can only be drawn in polygons with more than three vertices.
What are their types? A polygon with more than four corners can be convex or concave. The difference between the latter is that some of its vertices can lie on opposite sides of a straight line drawn through an arbitrary side of the polygon.
How to find the area of a regular and irregular hexagon?
- Knowing the length of the side, multiply it by 6 and get the perimeter of the hexagon: 10 cm x 6 = 60 cm
- Let's substitute the obtained results into our formula: Area = 1/2 * perimeter * apothem Area = ½ * 60cm * 5√3 Solving: Now it remains to simplify the answer in order to get rid of square roots, and indicate the result in square centimeters: ½ * 60 cm * 5√3 cm = 30 * 5√3 cm = 150 √3 cm = 259.8 cm² Video on how to find the area of a regular hexagon There are several options for determining the area of an irregular hexagon:
- Trapezium method.
- A method for calculating the area of irregular polygons using a coordinate axis.
- A method for splitting a hexagon into other shapes.
Depending on the initial data that you know, the appropriate method is selected.
Important
Some irregular hexagons are composed of two parallelograms. To determine the area of a parallelogram, multiply its length by its width and then add the two already known areas. Video on how to find the area of a polygon An equilateral hexagon has six equal sides and is a regular hexagon.
The area of an equilateral hexagon is equal to 6 areas of triangles into which a regular hexagonal figure is divided. All triangles in a hexagon of regular shape are equal, therefore, to find the area of such a hexagon, it will be enough to know the area of at least one triangle. To find the area of an equilateral hexagon, of course, use the area formula of a regular hexagon described above.
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Decorating a home, clothing, drawing pictures contributed to the formation and accumulation of information in the field of geometry, which people of those times obtained empirically, bit by bit, and passed on from generation to generation. Today, knowledge of geometry is necessary for a cutter, a builder, an architect and every ordinary person in everyday life. Therefore, you need to learn how to calculate the area of various shapes, and remember that each of the formulas can be useful later in practice, including the formula of a regular hexagon.
A hexagon is a polygonal shape with a total of six corners. A regular hexagon is a hexagonal shape that has equal sides. The angles of a regular hexagon are also equal to each other.
In everyday life, we can often find objects that have the shape of a regular hexagon.
Irregular polygon side area calculator
You will need
- - roulette;
- - electronic rangefinder;
- - a sheet of paper and a pencil;
- - calculator.
Instruction 1 If you need the total area of an apartment or a separate room, just read the technical passport for an apartment or house, it indicates the footage of each room and the total footage of the apartment. 2 To measure the area of a rectangular or square room, take a tape measure or electronic rangefinder and measure the length of the walls. When measuring distances with the rangefinder, be sure to observe the perpendicularity of the direction of the beam, otherwise the measurement results may be distorted. 3 Then multiply the resulting length (in meters) of the room by the width (in meters). The resulting value will be the floor area, it is measured in square meters.
Gaussian area formula
If you need to calculate the floor area of a more complex structure, for example, a pentagonal room or a room with a round arch, sketch out a sketch on a piece of paper. Then divide the complex shape into several simple ones, for example, a square and a triangle or a rectangle and a semicircle. Measure with a tape measure or rangefinder the size of all sides of the resulting figures (for a circle you need to find out the diameter) and enter the results on your drawing.
5 Now calculate the area of each shape separately. Calculate the area of rectangles and squares by multiplying the sides. To calculate the area of a circle, divide the diameter in half and square (multiply it by yourself), then multiply the resulting value by 3.14.
If you only need half a circle, divide the resulting area in half. To calculate the area of a triangle, find P, for this, divide the sum of all sides by 2.
Formula for calculating the area of an irregular polygon
If the points are numbered sequentially in the counterclockwise direction, then the determinants in the formula above are positive and the modulus in it can be omitted; if they are numbered in a clockwise direction, the determinants will be negative. This is because the formula can be viewed as a special case of Green's theorem. To apply the formula, you need to know the coordinates of the vertices of the polygon in the Cartesian plane.
For example, let's take a triangle with coordinates ((2, 1), (4, 5), (7, 8)). Take the first x-coordinate of the first vertex and multiply it by the y-coordinate of the second vertex, and then multiply the x-coordinate of the second vertex by the y of the third. We repeat this procedure for all vertices. The result can be determined using the following formula: A tri.
Formula for calculating the area of an irregular quadrangle
A) _ (\ text (tri.)) = (1 \ over 2) | x_ (1) y_ (2) + x_ (2) y_ (3) + x_ (3) y_ (1) -x_ (2) y_ (1) -x_ (3) y_ (2) -x_ (1) y_ (3) |) where xi and yi denote the corresponding coordinate. This formula can be obtained by opening the brackets in the general formula for the case n = 3. By this formula, you can find that the area of the triangle is equal to half the sum of 10 + 32 + 7 - 4 - 35 - 16, which gives 3. The number of variables in the formula depends on the number of sides of the polygon. For example, the formula for the area of a pentagon will use the variables up to x5 and y5: A pent. = 1 2 | x 1 y 2 + x 2 y 3 + x 3 y 4 + x 4 y 5 + x 5 y 1 - x 2 y 1 - x 3 y 2 - x 4 y 3 - x 5 y 4 - x 1 y 5 | (\ displaystyle \ mathbf (A) _ (\ text (pent.)) = (1 \ over 2) | x_ (1) y_ (2) + x_ (2) y_ (3) + x_ (3) y_ (4 ) + x_ (4) y_ (5) + x_ (5) y_ (1) -x_ (2) y_ (1) -x_ (3) y_ (2) -x_ (4) y_ (3) -x_ (5 ) y_ (4) -x_ (1) y_ (5) |) A for quadrilateral - variables up to x4 and y4: A quad.
