# PARAM VISIONS

All about civil construction knowledge- PARAM VISIONS

### Calculating the area of irregular shaped (5 side) land or plot or site./ Area calculation for the irregular pentagon-shaped land.( part- 3 )

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.

= √ 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.

= [√ 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.

Back ðŸ‘ˆ Part-2

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