1. There are several methods to calculate the area of land from survey data, including graphical, instrumental, and from field notes. 2. Common units for expressing area include square meters, hectares, square feet, and acres. 3. Key computational methods covered are the mid-ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's rule, which involve calculating the area based on ordinates or offsets taken at regular intervals along a baseline. 4. Each method makes different assumptions about the shape of the boundary between ordinates, with Simpson's rule assuming a parabolic arc to provide a more accurate result than the trapezoidal rule.

1. Er. Mital Damani

2.  INTRODUCTION
The term “area” in the context of surveying refers to the area of the tract
of land projected upon the horizontal plane and not to the actual area
of the land surface.
 Area may be expressed in the following units :
1 : Square meters
2 : Hectares (1 hectare =10000 m 2
=2471 acres)
3 : Square feet
4 : Acres (1 acre =4840 sq. yd. =43,560 sq. ft.)
5 : Square kilometer (km2) = (1 km2 =106 m2)

3. Computation of Area
Graphical Method Instrumental method
From Field notes
Entire area
Boundary area
Frotted planm plo
Mid oridnate rule
Trapezoidal rule
Simpson rule
Removable Disk (8GB).lnk
Avg. oridnate rule

4.  In this method, chain line
is run approximately in the
centre of the area to be
calculated. With the help
of the cross-staff or
optical square,

5.  Area of fig 1 can be calculated as
 A=A1+A2+A3+A4+A5
 A1=1/2(58-25)*10=165 m2
 A2=1/2(25*10)=125 m2
 A3=1/2(16*12)=96 m2
 A4=1/2(12+9)*(50-16)=357 m2
 A5=1/2(58-50)*9=36 m2
 Total area of field A=779 m2

6.  The area may be calculated in the following two ways.
 Case-1: considering the entire area:
 The entire area is divided into regions of a convenient shape
and calculated as follows:
 (1) by dividing the area into triangles.
 (2) by dividing the area into squares.
 (3) by drawing parallel lines and converting them to rectangles.

7.  Triangle area
=1/2*base*altitude
 Area=sum of areas of
triangles
 Each square represents unit
area 1 cm2 or 1 m2
 Area=nos. of square *unit
area

8.  Area =Σ Length of
rectangle ×Constant
depth

9.  In this method, a large square or
rectangle is formed within the
area in the plan. The ordinates
are drawn at regular intervals
from the side of the square to the
curved boundary.
 Total area A=Middle Area
A1+boundary area A2
 Middle area can be subdivided
into simple geometrical shapes ,
such as triangle rectangle ,
squares, trapezoids etc and Area
of these figures are determined
from the dimensions obtained
from the plan.

10. 1 The mid-ordinate rule
2 The average ordinate rule
3 The trapezoidal rule
4 Simpson rule
The mid ordinate Rule :
Let O1,O2,O3,….,On=Ordinate
At equal intervals .
l=length of base line
d=common distance between ordinates
h1,h2,….,hn=mid-ordinates
Area of plot=h1*d+h2*d+…+hn*d
=d(h1+h2+….+hn)
i.e. Area =common distance*sum of
mid-ordinates

11.  Lets O1,O2,…..,On=Ordinate or
offsets at regular intervals
 L=Length of base line
 n= Number of divisions
 n+=number of ordinates
 Area =O1+O2+….+On/n+1*l
 =sum of ordinates/no. of
ordinates *length of base line

12.  While applying the trapezoidal
rule, boundaries between the
ends of the ordinates are
assumed to be the straight.
Thus, the area enclosed
between the base line and the
irregular boundary line are
considered as trapezoids.

13.  Let O1,O2,….On = Ordinates at equal intervals
 d=Common distance
 1st
Area =O1+O2/2*d
 2nd
Area =O2+O3/2*d
 3rd
Area = O3+O4/2*d
 last area = On-+On/2*d
 Total area =[O1+2O2+2O3+2O4 +2On-1 +On]*d/2
 [O1+On+2(O2+O3+….+ On-1)]*d/2
 Common distance/2 [(1st
ordinate +last ordinate)+2 (sum of other ordinates)

14.  In this rule the boundaries between
the ends of ordinates are assumed to
form an arc of the parabola. Hence
Simpson rule is sometimes called the
parabola rule.
 Let O1,O2,O3=Three consecutive
ordinates
 d=Common distance between the
ordinates
 Area AF2DC = area of trapezium
AFDC+ Area of * segment F2DEF
Here,
 Area of trapezium =O1+O2/2*2d

15.  Area of segment =2/3*area of parallelogram F13D
 = 2/3 *E2*2d =2/3 *{O2-O1+O2/2}*2d
 So, the area between the first two divisions,
 ∆1=O1+O3/2*2d+2/3{O2-O1+O3/2}*2d
 =d/3(O1+4O2+O3)
 Similarly, the area between next two divisions
 ∆2= d/3(O3+4O4+O5) and so on .
 Total area =d/3 (O1+4O2+2O3+4O4+……+On)
 =d/3 [o1+on+4(o2+o4+…)+2(o3+o5+…)]
 =common distance/3[(1st
ordinate + last ordinate) + 4(sum of even
ordinates) + 2 (sum of remaining odd ordinates)]

16.  1. The boundary between the
ordinates is considered to be
straight
 2. There is no limitation . It can be
applied for any no. of ordinates.
 3. It gives an approximate result.
 1.The boundary between the
ordinates is considered to be an
arc of a parabola .
 2. This rule can be applied when
the no. of ordinates must be odd.
 3. It gives a more accurate result
than the trapezoidal rule…

17. A=M(FR – IR +/- 10N + C)