Name
Enrollment no
Roll no
PATEL KRUPALI
130840106040
06
SHAH JENNY
130840106056
61
NAYAK KHUSHBU
130840106025
78
GAMIT ZANKHANA
130840106015
49
Guided by
- Mr. Shivang Dabhi
-Miss Ankita Upadhyay
Area
 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 =2471 acres)
3 : Square feet
4 : Acres (1 acre =4840 sq. yd. =43,560 sq. ft.)
5 : Square kilometer (km2) = (1 km2 =106 m2)
2
Computation of Area
Graphical Method
From Field notes
Instrumental method
Frotted planm plo
Entire area
Boundary area
Mid oridnate rule
Avg. oridnate rule
Removable Disk (8GB).lnk
Trapezoidal rule
Simpson rule
COMPUTATION OF AREA FROM
FIELD NOTES:
 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,
 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
.Computation of area from a plotted plan
 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.
 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
 Area =Σ Length of
rectangle ×Constant
depth
Case 2 : Middle area +boundary
Area :
 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.
Boundary area is calculated according to one
of the following rules:
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
(2) The Average-Ordinate Rule :
 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
3: The Trapezoidal Rule :
 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.
 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)
4: Simpson Rule
 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
 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)]
TRAPEZOIDAL RULE V/S
SIMPSON RULE
 1. The boundary between the
 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.
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…
PLANIMETER
A=M(FR – IR +/- 10N + C)