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Faculty of Engineering Technology & Research. Isroli, Afwa .

Faculty of Engineering Technology & Research. Isroli, Afwa. 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.

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Faculty of Engineering Technology & Research. Isroli, Afwa .

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  1. Faculty of Engineering Technology & Research. Isroli, Afwa.

  2. 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 m2=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 Frotted planm plo Entire area Boundary area Mid oridnate rule Trapezoidal rule Simpson rule Avg. oridnate rule

  4. 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,

  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. .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.

  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. 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.

  10. 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

  11. (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

  12. 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.

  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. 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

  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. TRAPEZOIDAL RULE V/S SIMPSON RULE • 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. PLANIMETER A=M(FR – IR +/- 10N + C)

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