If you are a surveyor or owner of land in which you want to calculate the area of land then, you are at the right place. There are always common problems found in the surveyor or students to find out the area of an irregular land.

If the land is in square rectangular, triangular then we can easily find the area of land using simple geometrical formula. we will discuss how can we calculate the area of all types of land one by one.

All plots or land are not in fix geometrical shapes like a triangle, rectangle, or square. So, we often have to face difficulties to calculate the area of these kinds of land which are not in fixed geometrical shape.

Let us describe and make clear sense among all probable types and shapes of land which generally we have to calculate.

### 1) Triangular Plots or Land

These types of land are rarely found, but it does not mean that you will not have to face this problem. you can probably get these types of land at the corner of road edge ar turning point. so let us solve shortly these types of problem.

#### Q) Calculate the area of given triangular land having side 21 m, 13 m, and 20 m respectively.

Solution:-

Let, Given side of triangle be,

(AB) = (a) = 21 meter

(AC) = (b) = 21 meter

(AB) = (c) = 21 meter

We have,

So, at first calculate semi perimeters (s) = (a+b+c)/2 = (20+21+13)/2 = 27 m.

The Semiperimeter of the triangle is half of its perimeter i.e (sum of their sides).

Now using above formula we get,

Area of triangular land (A)

Hence, in this way we can calculate area of land which are in triangular shape. now let us calculate area of rectangular plots of land.

### 2) Rectangular Plots or Land

These types of land are often found in all areas. The sides of land whose one side is equal to their 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. Let’s understand with the help of numerical and figure given below.

#### Q) Calculate the area of rectangular land having dimensions given in the figure below.

Solution, Here in the figure two sides are 14 meter and two side are 8 meter.

so, let Length (L) = 14 meter and Breadth (B) = 8 meter

We have,

So, Using above formula we get,

**Area = L X B = (14 X 8) = 112 m ^{2} **

Hence, in this way we can calculate area of land which are in rectangular shape. now let us calculate area of square plots or land.

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### 3) Square Plots or Land

These types of land are also common in all areas. you will get the shape of land mostly and nearly in rectangular or in square shape. The sides of land whose all sides are equal to each other are known as square land.

It’s all sides are perpendicular to each other i.e 90 degrees with each other. Let’s understand with the help of numerical and figure given below.

#### Q) Calculate the area of square land having dimensions given in the figure below.

Solution, Here in the figure have all sides equal and 8 meters.

so, let Length (L) = 8 meter

We have,

Using above formula,

Area of Land (A) = (8 X 8 ) **m ^{2}** = 64

**m**

^{2}Hence, in this way, we can calculate the area of land which is in square in shape. now let us calculate the area of trapezium plots or land.

### 4) Trapezium land

This type of land may be regular or may be irregular. I am describing here all types of land with examples. let us discuss all land with the help of figure and formula to calculate it.

**A)** Land having two side parallel to each other

These types are land is found at the side of the road edge and maybe made artificially for a different purpose. In this type of land two sides are parallel to each other but the other two sides are not. Let us understand with an example.

You can also calculate the area of above land by dividing land into two parts in rectangle and triangle which you can see in the figure by the green line.

After that you can again use formula of square and triangle to each other and get total area.

I hope you understood and you can calculate the area of these types of land. Let us see another type of irregular land which you generally found at the survey. but don’t worry I will do the numerical of this land also. so let us move forward.

**B)** Land having no any side parallel to each other

This type of land is mostly found in every place of state and country. This is irregular land. In these types of land, all sides are different from each other. and also they make different angles with each other.

Surveyors have to calculate these types of land so, often and they get more problems in such types of land to calculate actual area. let us understand with numerical and formula to calculate the area of land.

#### Q) Calculate the area of irregular land having dimension given in the figure below.

Solution,

To calculate these types of land is very easy. to find out the area of these types of land, first of all, burry four pegs or ranging rods at all corners of the land. after that take measurements of all sides of the land. and keep in mind you must take the measurement of any one of the diagonal plots.

Now, you can see in the figure, total land has been divided into two parts with blue line diagonals and they are triangles in shape.

That’s all, use the formula of triangular land separately and add both to get the total area. isn’t it easy?

Now, let us move on 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 **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 value we get Area of triangle BDC,

= 30 **m ^{2}**

Hence total are of land become,

= Area of triangle ABD and triangle BDC

= A_{1} + A_{2}

= (6 + 30) **m ^{2}**

= 36 **m ^{2}**

How did you find the 5m of BD?