**If you are looking for a readymade calculator for type-5 land, then** **click here.**

** For the calculation procedure, go through the following steps.ðŸ‘‡**

Now, let us go through irregularly shaped land or plot, having 5 sides, and let us calculate the area of this plot, by using mathematical formulas.

**Type - 5:**

Here, all 5 sides of the land are unequal in length & are not parallel to each other.

__Given data:__

Side AB = 20' 3" = 20.25 ft.

Side BC = 35' 4" = 35.333 ft.

Side CD = 40' 5" = 40.416 ft.

Side DE = 24' = 24.0 ft.

Side EA = 23' 7" = 23.583 ft.

**Note:**

1. For your understanding, all the dimensions of the **type-5** drawing are taken in ft. & in the first 4 types of land drawing, we have taken meters as a measuring unit.

2. We have converted all the land measurements into ft. by dividing inches by 12 (1 ft.=12 inch).

To calculate the area of 5-sided or pentagon-shaped land, we have to practically measure the distance between AD, & BD as shown in the above drawing.

Side AD = 40' 2" = 40.166 ft. as measured on-site.

Side BD = 43' 4" = 43. 333 ft. as measured on-site.

**Note**: You can measure the distance between AD & BD by plotting the land drawing on a proportionate scale, but the result may not be that accurate.

Now, we will calculate the area of triangle ADE, triangle ABD, & triangle BCD separately.

We will use **Heron's formula** to calculate the areas.

__1. Area of triangle ADE__

= √ s (s - a ) ( s - b ) ( s - c )

Here, s is the semi-perimeter of the triangle

i.e. s = [(a + b + c) / 2]

a, b, and c are the 3 sides of the triangle.

By data input

s = [(side EA + side DE + side AD) / 2]

= [(23.583 + 24 + 40.166) / 2]

= [87.749 / 2]

= **43.874 ft.**

**Area of triangle ADE**

= [√ 43.874 ( 43.874 - 23.583) ( 43.874 - 24 ) ( 43.874 - 40.166 )]

= [√ 43.874 ( 20.291 ) ( 19.874 ) ( 3.708 )]

= [√ 65,604.812]

= **256.134 sqft.**

__ 2. Similarly, the area of triangle ABD__

= √ s (s - a ) ( s - b ) ( s - c )

s = [(side AB + side BD + side AD) / 2]

= [(20.25 + 43.333 + 40.166) /2]

= [103.749/ 2]

=** 51.874 ft.**

**Area of triangle ABD**

= [√ 51.874 ( 51.874 - 20.25) ( 51.874 - 43.333 ) ( 51.874 - 40.166 )]

= [√ 51.874 × 31.624 × 8.541 × 11.708]

= [√ 164,043.103]

= **405.022 sqft.**

__ 3. Area of triangle BCD__

= √ s (s - a ) ( s - b ) ( s - c )

s = [(side BC + side CD + side BD) / 2]

= [(35.333 + 40.416 + 43.333) /2]

= [119.082/ 2]

=** 59.541 ft.**

**Area of triangle BCD **

= [√ 59.541 ( 59.541 - 35.333) ( 59.541 - 40.416 ) ( 59.541 - 43.333 )]

= [√ 59.541 × 24.208 × 19.125 × 16.208]

= [√ 446,792.534]

= **668.425 sqft.**

Now, the total __area of land ABCDE__

= [Area of triangle ADE + area of triangle ABD + area of triangle BCD]

= [256.134 sqft. + 405.022 sqft. + 668.425 sqft.]

= **1329.581 sqft.**

**Note:**

By using Heron's formula, you can calculate the area of all types of irregular-shaped land or plots having an **'n'** number of sides.

**Thank you for going through this calculation❤. Have a good dayðŸ˜„**

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