Area calculation

Area is divided into triangles, rectangles, squares or trapeziumsArea of the one figure (e.g. triangles, rectangles, squares or trapeziums) is calculated and multiplied by total number of figures.Area along the boundaries is calculated as

Total area of the filed=area of geometrical figure + boundary areas

Problem-1

Problem 1-Result

Computation of area from plotted planBoundary area can be calculated as one of the following rule:The mid-ordinate ruleThe average ordinate ruleThe trapezoidal ruleSimpsons rule

Mid-ordinate rulel

Average ordinate rule

Trapezoidal rule

Simpsons rule

ProblemsThe following perpendicular offsets were taken from chain line to an irregular boundary:Chainage 0 10 25 42 60 75 moffset 15.5 26.2 31.8 25.6 29.0 31.5Calculate the area between the chain line, the boundary and the end offsets.

The following perpendicular offsets were taken from a chain line to a hedge:

Calculate the area by mid ordinate and Simpsons rule.

chainage0153045607080100120140offsets7.68.510.712.810.69.58.37.96.44.4

Area by double meridian distancesMeridian distance of any point in a traverse is the distance of that point to the reference meridian, measured at right angle to the meridian.The meridian distance of a survey line is defined as the meridian distance of its mid point. The meridian distance sometimes called as the longitude.

1234ABCDMid pointsMeridian distance of points (d1, d2, d3, d4)d1/2d1/2d2/2d2/2d3/2d3/2d4/2d4/2m1m2m3m4dcb

Meridian distances of survey line:m1=d1/2m2= m1+d1/2+d2/2m3=m2+d2/2-d3/2m4=m3-d3/2-d4/2Area by latitude and meridian distanceArea of ABCD=area of trapezium CcdD + area of trapezium CcbB area of triangle AbB area of triangle AdD= m3*L3+ m2*L2-1/2*2*m4*L4-1/2*2*m1*L1=m3*L3+m2*L2-m4*L4-m1*L1

Double meridian distance:M1= meridian distance of point A + meridian distance of point BM1=0+d1M2=meridian distance of point B + meridian distance of point C=d1+(d1+d2)=M1+(d1+d2) M3=(d1+d2)+(d1+d2-d3)

Area of the traverse ABCD = M3*L3+M2*L2-M1*L1-M4*L4

Area by Co-Ordinates

The following table gives the corrected latitudes and departures (in m) of the sides of a closed traverse ABCD. Compute the area by (a) M.D. method (b) co-ordinate method

SideLatitudeDepartureNSEWAB1084BC15249CD1234DA0257

Volume calculationFrom cross sectionsFrom spot levelsFrom contours

Measurement of volume3 methods generally adopted for measuring the volume are(i) from cross sections(ii) from spot levels(iii) from contours

Methods of volume calculationA1A2B2D2C2B1D1C1A1A2B2B1D2C2D1C1 Prismoidal method

Also called Simpsons rule for volume. Necessary to have odd number of cross sections.What if there are even number of C/S?

Trapezoidal method:Assumption mid area is mean of end areas.Volume =d{(A1+An)/2+A2+A3++An-1}

A railway embankment is 10 m wide with side slopes 1.5:1. assuming the ground to be level in a direction transverse to the centre line, calculate the volume contained in a length of 120 m, the centre heights at 20 m intervals being in metres 2.2, 3.7, 3.8, 4.0, 3.8, 2.8, 2.5.A railway embankment 400 m long is 12 m wide at the formation level and has the side slope 2:1. The ground levels across the centre line are as under:

The formation level at zero chainage is 207.00 and the embankment has a rising gradient of 1:100. The ground is level across the centre line. Calculate the volume of earthwork.

Distance0100200300400R.L.204.8206.2207.5207.2208.3