Chapter 7: Computation of Area

ch-7 page 207 pb-1

In [1]:
from __future__ import division

import math


print('chainage 0 and 20')
a1=0;b1=20;

base=b1-a1;
o1=0;o2=42;
mo1=(o2+o1)/2;

ae1=base*mo1;
print('area=',ae1);

print('chainage 20 and 65')
a1=20;b1=65;

base=b1-a1;
o1=58;o2=42;
mo2=(o2+o1)/2;

ae2=base*mo2;
print('area=',ae2);


print('chainage 65 and 110')
a1=65;b1=110;

base=b1-a1;
o1=0;o2=58;
mo3=(o2+o1)/2;

ae3=base*mo3;
print('area=',ae3);


print('chainage 90 and 110')
a1=90;b1=110;

base=b1-a1;
o1=0;o2=60;
mo4=(o2+o1)/2;

ae4=base*mo4;
print('area=',ae4);

print('chainage 40 and 90')

a1=40;b1=90;

base=b1-a1;
o1=60;o2=20;
mo5=(o2+o1)/2;

ae5=base*mo5;
print('area=',ae5);

print('chainage 0 and 40')
a1=0;b1=40;

base=b1-a1;
o1=20;o2=0;
mo6=(o2+o1)/2;

ae6=base*mo6
print('area=',ae6);


area=ae1+ae2+ae3+ae4+ae5+ae6;

print('area of field =',area);

chainage 0 and 20
('area=', 420.0)
chainage 20 and 65
('area=', 2250.0)
chainage 65 and 110
('area=', 1305.0)
chainage 90 and 110
('area=', 600.0)
chainage 40 and 90
('area=', 2000.0)
chainage 0 and 40
('area=', 400.0)
('area of field =', 6975.0)

ch-7 page 209,210 pb-2

In [2]:
from __future__ import division

import math


print('chainage 15.5 and 27.5')
a1=15.5;b1=27.5;

base=b1-a1;
o1=0;o2=22.5;
mo1=(o2+o1)/2;

ae1=base*mo1;
ap1=0;
an1=ae1;
print('area=',ae1);

print('chainage 15.5 and 50')
a1=15.5;b1=50;

base=b1-a1;
o1=22.5;o2=30;
mo2=(o2+o1)/2;

ae2=base*mo2;
ap2=ae2;
an2=0;
print('area=',ae2);


print('chainage 50 and 75.5')
a1=50;b1=75.5;

base=b1-a1;
o1=30;o2=35.5;
mo3=(o2+o1)/2;

ae3=base*mo3;
ap3=ae3;
an3=0;
print('area=',ae3);


print('chainage 75.5 and 86.7')
a1=75.5;b1=86.7;

base=b1-a1;
o1=35.5;o2=0;
mo4=(o2+o1)/2;

ae4=base*mo4;
ap4=ae4;
an4=0;
print('area=',ae4);

print('chainage 86.7 and 90')

a1=86.7;b1=90;

base=b1-a1;
o1=0;o2=10.5;
mo5=(o2+o1)/2;

ae5=base*mo5;
ap5=0;
an5=ae5;
print('area=',ae5);

print('chainage 60 and 90')
a1=60;b1=90;

base=b1-a1;
o1=10.5;o2=25.0;
mo6=(o2+o1)/2;

ae6=base*mo6
ap6=ae6;
an6=0;
print('area=',ae6);

print('chainage 35.5 and 60')
a1=35.5;b1=60;

base=b1-a1;
o1=25;o2=15;
mo7=(o2+o1)/2;

ae7=base*mo7
ap7=ae7;
an7=0;
print('area=',ae7);

print('chainage 27.5 and 35.5')
a1=27.5;b1=35.5;

base=b1-a1;
o1=15;o2=0;
mo8=(o2+o1)/2;

ae8=base*mo8
ap8=ae8;
an8=0
print('area=',ae8);

an=an1+an2+an3+an4+an5+an6+an7+an8;
ap=ap1+ap2+ap3+ap4+ap5+ap6+ap7+ap8;

area=ap-an;
print('ap,ae=',ap,an)
print('total area of field =',area);

chainage 15.5 and 27.5
('area=', 135.0)
chainage 15.5 and 50
('area=', 905.625)
chainage 50 and 75.5
('area=', 835.125)
chainage 75.5 and 86.7
('area=', 198.80000000000004)
chainage 86.7 and 90
('area=', 17.324999999999985)
chainage 60 and 90
('area=', 532.5)
chainage 35.5 and 60
('area=', 490.0)
chainage 27.5 and 35.5
('area=', 60.0)
('ap,ae=', 3022.05, 152.325)
('total area of field =', 2869.7250000000004)

ch-7 page 214 pb-1

In [3]:
from __future__ import division

import math


dis=10;
a=0;g=0;
b=2.5;c=3.5;d=5;e=4.6;f=3.2;

print('Mid ordinate rule');

h1=(a+b)/2;
h2=(b+c)/2;
h3=(c+d)/2;
h4=(d+e)/2;
h5=(e+f)/2;
h6=(f+g)/2;
area=dis*(h1+h2+h3+h4+h5+h6);

print('required area is',area,'square meters');

print('average ordinate rule');
dis=10;
p=6;
bl=dis*p;
no=7;


area2=bl*(a+b+c+d+e+f+g)/no;

print('required area is',area2,'sqare meters');

print('trapezoidal rule');


area3=(dis/2)*(2*(a+b+c+d+e+f+g));

print('required area is ',area3,'square meters');
print('simpsons rule');

area4=(dis/3)*(4*(b+d+f)+2*(c+e));
print('required area is ',area4,'square meters');

Mid ordinate rule
('required area is', 188.0, 'square meters')
average ordinate rule
('required area is', 161.14285714285714, 'sqare meters')
trapezoidal rule
('required area is ', 188.0, 'square meters')
simpsons rule
('required area is ', 196.66666666666669, 'square meters')

ch-7 page 216 pb-2

In [4]:
#ch-7 page 216   pb-2
from __future__ import division

import math

print('trapezoidal rule');

o1=3.5;o2=4.3;o3=6.75;o4=5.25;o5=7.5;o6=8.8;o7=7.9;
o8=6.4;o9=4.4;o10=3.25;

dis=15;

area1=(dis/2)*(o1+o10+(2*(o2+o3+o4+o5+o6+o7+o8+o9)));

print('required area is ',area1,'square meters');

print('simpsons rule')

A1=dis/3*(o1+o9+4*(o2+o4+o6+o8)+2*(o3+o5+o7));

A2=dis/2*(o10+o9);

area2=A1+A2;
print(A1,A2)

print('required area is ',area2,'square meters');

trapezoidal rule
('required area is ', 820.125, 'square meters')
simpsons rule
(756.0, 57.375)
('required area is ', 813.375, 'square meters')

cha 7 page -216 pb-3

In [5]:
from __future__ import division

import math

o1=2.5;o2=3.8;o3=4.6;o4=5.2;o5=6.1;o6=4.7;o7=5.8;o8=3.9;o9=2.20;

d1=5;
d2=10;
d3=20;


print('trapezoidal rule')

del1=(d1/2)*(o1+o5+2*(o2+o3+o4));
del2=(d2/2)*(o5+o7+2*(o6));
del3=(d3/2)*(o7+o9+2*(o8));

total1=del1+del2+del3;
print(del1,del2,del3)

print('total area=',total1,'meters');

print('simpsons rule')

de1=(d1/3)*(o1+o5+4*(o2+o4)+2*(o3));
de2=(d2/3)*(o5+o7+4*(o6));
de3=(d3/3)*(o7+o9+4*(o8));


total2=de1+de2+de3;
print(de1,de2,de3)

print('total area is ',total2,'meters')

trapezoidal rule
(89.5, 106.49999999999999, 158.0)
('total area=', 354.0, 'meters')
simpsons rule
(89.66666666666667, 102.33333333333333, 157.33333333333334)
('total area is ', 349.33333333333337, 'meters')

cha 7 page -225 pb-1

In [6]:
#cha 7 page -225 ;pb-1

from __future__ import division

import math

ir=9.377;
fr=3.336;
m=100;
c=23.521;

n=1;

a1=m*(fr-ir+10*(n)+c);

a2=m*(fr-ir-10*(n)+c);

print('A=',a2);
print('required area is',a2,'meters');

('A=', 748.0)
('required area is', 748.0, 'meters')

cha 7 page -225,226 pb-2

In [7]:
from __future__ import division

import math

ir=8.652;
fr=6.798;
c=20;
m=100;
n=1;

sc=100;

a2=m*(fr-ir-10*(n)+c);

a2=a2*sc;

print('A=',a2);
print('required area is',a2,'meters');

('A=', 81460.00000000001)
('required area is', 81460.00000000001, 'meters')

cha 7 page -226 pb-3

In [8]:
from __future__ import division

import math

ir=4.855;
fr=8.754;
m=100;

n=0;
c=0;
sc=25
a=m*(fr-ir)
a=a*sc;
print('required area is',a,'meters');

('required area is', 9747.499999999998, 'meters')

cha-7 page-226 pb-4

In [9]:
from __future__ import division

import math

print('case 1')

ir=3.415;
fr=4.415;
n=0;
c=0;
sc=16;   #1cm^2=16m^2;
h=10000;
ag=0.16*h;

am=ag/sc;
print('A=',am);

m=am/(fr-ir);

print('M=',m);

print('case 2');

fr_ir=2.25;
c=21.22;
n=1

a1=m*(fr_ir-10+c);
print('required area is',a1);

area=m*c;

print('area of zero circle is',area);

case 1
('A=', 100.0)
('M=', 100.0)
case 2
('required area is', 1347.0)
('area of zero circle is', 2122.0)

cha-7 page-227 pb-5

In [10]:
from __future__ import division

import math

l=10;b=15;
a1=l*b;

ir=0.686;
fr=9.976;
n=2;
m=100;

marea=150;

c=(marea/100)+10.710;

area=m*c;
print('area of zero circle is',area,'square centimeters');

('area of zero circle is', 1221.0, 'square centimeters')

cha-7 page-228 pb-6

In [11]:
from __future__ import division

import math

print('case 1')
n=1;
c=0;
m=100;
fr=4.825;
ir=7.775;
area1=m*(fr-ir+10*n)

print('area of figure is',area1,'square cm');

print('case 2')
fr=8.755;
ir=2.325;
m=100;
n=2;
area2=m*(fr-ir-10*n+c)

print('area of figure is',area2,'sq cm')
c=(area1/m)+13.570;
print('C=',c)

areac=m*c;
print('area of zero circle is',areac,'square cm');

case 1
('area of figure is', 705.0, 'square cm')
case 2
('area of figure is', -1357.0, 'sq cm')
('C=', 20.62)
('area of zero circle is', 2062.0, 'square cm')