How to Calculate Area of land or Plot Which is Irregular in Shape

How to Calculate Area of land or Plot Which is Irregular in Shape

In this article, I will show you how to calculate the area of a plot that is regular or irregular in shape. And I am sure that, after viewing this article you can easily measure any type of plot area which are irregular in shape.

Surprisingly, you can measure the area of a plot of any size by using just two formulas. These two formulas are

a) ‘Area of a triangle’ formula

Area of triangle [latex] (A) = \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Where, s = semi-perimeter, and a, b, c, are the side of a triangle. The value of this semi-perimeter is = (sum of three sides)/ 2 = [latex] \frac{(a+b+c)}{2} [/latex]

b) ‘Area of rectangle’ formula

Area (A) = w×z

1. Regular Triangular shaped plot

Regular Triangular shaped plot or we can say the plot having 3 sides equal in length

By using General Formula:

As you can see in this picture there is a plot that is triangular in shape and each side of which is equal in length. Although, The rules for finding the area of an equilateral triangle are what we learned in school.

Area of equilateral triangle is = [latex] \frac{ \sqrt{3}}{4} \times (Side\, of \, the\, triangle)^{2} [/latex]
Therefore, the area of this plot will be = [latex] \frac{ \sqrt{3}}{4} \times (10)^{2} [/latex] = 43.3 m²

By using Common Formula:

Area of triangle [latex] (A) = \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Where, S = (10+10+10)/2 = 15

Therefore, the area of this triangular plot will be(A) = [latex] \sqrt{15(15-10)(15-10)(15-10)} [/latex]

Or, A = [latex] \sqrt{15(5)(5)(5)} [/latex]

Or, A = [latex] \sqrt{1875} [/latex]

Or, A = 43.3 m²

2. Irregular Triangular shaped plots or lands

Irregular Triangular shaped plot or we can say the plot having 3 sides different in length.

Case 1. When 2 sides are equal in length and 1 side is different.

As you can see in this picture, there are two sides that are equal in length, but 1 side is different from the others.

By using Common Formula:

Area of the triangle [latex] (A) = \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Where, S = (12+`12+18)/2 = 21

Therefore, the area of this type of plot will be(A) = [latex] \sqrt{21(21-12)(21-12)(21-18)} [/latex]

Or, A = [latex] \sqrt{21(9)(9)(3)} [/latex]

Or, A = [latex] \sqrt{5103} [/latex]

Or, A = 71 m²

Case 2: When all sides of a triangle are unequal in length.

As you can see in this picture, there are 3 sides, that are unequal in length.

By using Common Formula:

Area of the triangle [latex] (A) = \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Where, S = (9+`12+14)/2 = 17.5

Therefore, the area of this type of plot will be(A) = [latex] \sqrt{17.5(17.5-9)(17.5-12)(17.5-14)} [/latex]

Or, A = [latex] \sqrt{17.5(8.5)(5.5)(3.5)} [/latex]

Or, A = [latex] \sqrt{2863.44} [/latex]

Or, A = 53.51 m²

3. Square Plot or Land

It is very easy to calculate the area of the square-shaped lands or plots. I’m sure most of the readers know how to calculate the area of a square land.

The area of a square land is = a.a = 15.15 = 225 square meter or 2421.88 sqft

Example:

A land having 4 sides length is 35 ft, calculate the area of this plot or land in square meters.

The area of this square land is = a.a = 35.35 = 1225 sqft

We know,

[ 1 square feet = 0.092903 square meter]

Therefore, The area of this land in square meters will be = 1225*0.092903 = 113.8 m²

4. Rectangular Plots or lands

The formula used for the rectangular plot or land area is = w.z ( show fig.2)

Example:

Following is a rectangular-shaped land, calculate the area of the land

The area of this rectangular-shaped land will be = w.z = 20*30 = 600 square meters.

Read Also: Standard Room Sizes.

5. Trapizium shaped lands or plots

By using the general formula

Area of a trapezium = 0.5 × ( sum of two parallel lines) × height

Now, how to calculate height(h) in this particular case? There are two ways to calculate this height. You can measure it in the field directly, or you can calculate it by using the Pythagorean formula.

By using the Pythagorean theorem:

Given,

BE = 10 m.
AB = EF = 8 m.
CD = 10 m (BE = CD)
AC = DF = 3 m.

Pythagorean theorem is, AC² + BC² = AB²

Or, 3² + h² = 8²

Or, h² = 8² – 3²

Or, h = 7.42 m

Now, The area of this land will be = 0.5 × (16+10) × 7.42 = 96.46 m²

But the easy way will be you measure the value of h in the field directly with the help of a tape or chain. after that, put the value of h in the above equation.

Can we find its area using common formula? Yes, we can. we can divide this into two triangles as you can see in the below image. Only you need to measure the value of the AE line in the field by using measuring tape. After that, you can find out the area of this section by using this formula; Area of the triangle [latex] (A) = \sqrt{s(s-a)(s-b)(s-c)} [/latex]

6. Irregular Quadrilateral shaped plots or lands

Following is an irregular quadrilateral shaped land, or we can say the land having 4 sides with unequal length, or, irregular rectangular shaped land, calculate the area of this land.

As we can see in this picture, there are 4 sides, and each side’s length is different from the other. In this case, we need to divide this land into two different triangles as below image. After that, we can easily determine their area by using the common formula of a triangle. Let’s assume P is = 14 m.

The are of this quadrilateral will be = Area of (1) triangle + Area of (2) triangle

Semi perimeter for 1 no triangle s₁ is = (9+16+14)/2 = 19.5

Area of 1 no triangle A₁ is = [latex] \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Or, A₁ = [latex] \sqrt{19.5(19.5 – 9)(19.5 – 16)(19.5 – 14)} [/latex]

Or, A₁ = [latex] \sqrt{19.5(10.5)(3.5)(5.5)} [/latex]

Or, A₁ = [latex] \sqrt{3941.4} [/latex]

Or, A₁ = 62.7 m²

Semi perimeter for 2 no triangle s₂ is = (14+8+11)/2 = 16.5

Area of 2 no triangle A₁ is = [latex] \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Or, A₂ = [latex] \sqrt{16.5(16.5 – 14)(16.5 – 8)(16.5 – 11)} [/latex]

Or, A₂ = [latex] \sqrt{16.5(2.5)(8.5)(5.5)} [/latex]

Or, A₂ = [latex] \sqrt{1928.4} [/latex]

Or, A₂ = 43.91 m²

So, the area of this irregular quadrilateral shaped land or plot is = 62.7+43.91 = 106.61 m²

7. Irregular pentagonal shaped lands or plots

Following is an irregular pentagonal shaped land, or we can say the land has 5 sides with unequal lengths, calculate the area of this land.

As we can see in this picture, there are 5 sides, and each side’s length is different from the other. In this case, we need to divide this land into three different triangles as below image. After that, we can easily determine their area by using the common formula of a triangle.

Let’s assume P is 14 m, and Q is 13 m.

The area of this pentagon will be = Area of (1) triangle + Area of (2) triangle + Area of (3) triangle

Semi perimeter for 1 no triangle s₁ is = (13+6+14)/2 = 16.5

Area of 1 no triangle A₁ is = [latex] \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Or, A₁ = [latex] \sqrt{16.5(16.5 – 13)(16.5 – 6)(16.5 – 14)} [/latex]

Or, A₁ = [latex] \sqrt{16.5(3.5)(10.5)(2.5)} [/latex]

Or, A₁ = [latex] \sqrt{1515.9} [/latex]

Or, A₁ = 38.9 m²

Semi perimeter for 2 no triangle s₂ is = (14+14+13)/2 = 20.5

Area of 2 no triangle A₁ is = [latex] \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Or, A₂ = [latex] \sqrt{20.5(20.5 – 14)(20.5 – 14)(20.5 – 13)} [/latex]

Or, A₂ = [latex] \sqrt{20.5(6.5)(6.5)(7.5)} [/latex]

Or, A₂ = [latex] \sqrt{6495.9} [/latex]

Or, A₂ = 80.59 m²

Semi perimeter for 3 no triangle s₃ is = (13+2+14)/2 = 14.5

Area of 3 no triangle A₃ is = [latex] \sqrt{s(s-a)(s-b)(s-c)} [/latex]

Or, A₃ = [latex] \sqrt{14.5(14.5 – 13)(14.5 – 2)(14.5 – 14)} [/latex]

Or, A₃ = [latex] \sqrt{14.5(1.5)(12.5)(0.5)} [/latex]

Or, A₃ = [latex] \sqrt{135.9} [/latex]

Or, A₃ = 11.6 m²

So, the area of this irregular pentagonal shaped land or plot is = 38.9 + 80.59 + 11.6 = 131.09 m²(square meter)

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