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If you are a surveyor or the owner of the land you wish to know how to calculate area of land. If the land is square rectangular, or triangular then we can quickly calculate the area of the land utilizing simple geometrical formulas.
All plots of land are not available in fixed geometrical shapes like a triangle, rectangles, or squares. So, we usually have to face many difficulties to determine the area of these types of land that are not in fixed geometrical shape.
1. Triangular Land
These types of land are not found commonly, but it does not mean that it doesn’t exist you will have to face this problem. These types of lands are seen at the corner of the road end at a turning point. Calculating an Area of Land like this is slightly difficult.
a. Numerical
Solution:
Let, Given side of the triangle be,
(AB) = (a) = 20 meter
(AC) = (b) = 18 meter
(AB) = (c) = 15 meter
Area of scalene triangle in terms of three sides,
Area of triangle (A)= √s(s-a)(s-b)(s-c)
where,
s= semi-perimeter
a= Length of the first side
b= length of the second side
c= length of the third side
We have,
So, at first, calculate semi-perimeters (s) = (a+b+c)/2 = (20+18+15)/2 = 26.5 m.
The Semiperimeter of the triangle is half of its perimeter i.e. (the sum of their sides).
Now using the above formula we get,
Area of triangular land (A) = √26.5(26.5-20) (26.5-18) (26.5-15)
A= 129.76 m^{2}
We can determine the area of land which is in a triangular shape. Now let us calculate area of land that are rectangular plots.
3. Rectangular Land
These types of land are usually available in all places. Those land in which one side is equal to the opposite side and another side is equal to another side are known as rectangular land.
It’s all sides are perpendicular to each other i.e. 90 degrees with each other.
Numerical
The solution, Here in the figure two sides are 12 meters and two sides are 6 meters.
so, let Length (L) = 12 meter and Breadth (B) = 8 meter
We have,
So, Using the above formula we get,
Area = L X B = (12 X 8) = 96 m^{2}
Hence, in this way, we can calculate the area of land which is in a rectangular shape. now let us calculate the area of square plots of land.
4. Square Plots or Land
These types of land are also commonly seen in all places. You will see the shape of this land majorly and nearly rectangular or in square shape. The sides of land whose all sides are equal are known as square land.
It’s all sides are perpendicular to each other i.e. 90 degrees with each other.
a. Numerical
The solution, Here in the figure has all sides equal and 10 meters.
so, let Length (L) = 10 meter
We have,
By using the formula,
Area of Land (A) = (10 X 10) m^{2} = 100 m^{2}
Hence, in this way, we can calculate the area of land which is square in shape. now let us calculate the area of trapezium plots or land.
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5. Trapezium land
This type of land can be seen as either regular or irregular.
A. Land Having Two Side Parallel to Each Other
These types of land are seen at the side of the road edge and may be prepared artificially for various aims. In this type of land, two sides are parallel to each other but the other two sides are not parallel.
We can also determine the area of the above land by dividing land into two parts in rectangle and a triangle which is shown in the figure.
After that, you can again use the above formula of square and triangle to calculate each other and calculate the total area.
B. Land Having No Side Parallel to Each Other
This type of land is majorly available in different places (state and country). This is irregular land. In these types of land, all sides vary from each other. and also they have various angles with each other.
i. Numerical
Solution,
Calculating the area of land of these types is very quick and easy. To calculate the area of these types of land, first of all, plot 4 pegs or ranging rods at all corners of the land.
After that take measurements of all sides of the land by using tape. Don’t forget to take the measurement of any one of the diagonal plots.
Now, you can watch in the figure, the total land has been separated into two parts with that blue line diagonals and they are triangles in shape.
Now, let us move on to calculation,
In triangle ABD,
let, BD (a) = 5 meter, AD (b) = 3 meter, AB (c) = 4 meter
Again we have,
where, S = (a+b+c)/2 = (5 + 3 + 4)/2 = 6 meter.
So, Putting all values we get the Area of triangle ABD,
A_{1}= √6(6-5)(6-3)(6-4)
A_{1} = 6 m^{2}
In the same way, for triangle BDC,
let, DC (a) = 13 meter, BC (b) = 12 meter, BD (c) = 5 meter
where, we have (S) = (a+b+c)/2 = (13 + 12 + 5)/2 = 15 meter.
So, putting all values we get the Area of triangle BDC,
A_{2}= √ 15(15-13)(15-12)(15-5)
= 30 m^{2}
Hence the total area of land become,
= Area of triangle ABD and triangle BDC
= A_{1} + A_{2}
= (6 + 30) m^{2}
= 36 m^{2}
Hence, in this way, we can determine the area of land which is irregular in shape.
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