Course
Year
: S0663 – Land Surveying
: 2007
Session 9
AREA MEASUREMENT
Area Measurement Methods
• Graphical Measurement
• Analytical Measurement
• Measurement using Area Measuring Apparatus
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Area Measurement Methods
• Graphical Measurement
– Using graphical paper
• Analytical Measurement
–
–
–
–
Triangle Approaching
Coordinate Approaching
Trapezoidal Approaching
Simpson Approaching
• Measurement using Area Measuring Apparatus
– Planimeter
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The Using of Graphical Paper
• Just for rough estimation
• The analysis area is drawn at graphical paper with
defined scale
• The area is determine by counting the amount of
sections or boxes
• The accuracy will be increased if the section or box size
smaller
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The Using of Graphical Paper (1)
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The Using of Graphical Paper (1)
Section size = 1 m2
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The Using of Graphical Paper (1)
160 sections
Section size = 1 m2
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The Using of Graphical Paper (1)
60 sections
160 sections
Section size = 1 m2
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The Using of Graphical Paper (1)
60 sections
160 sections
Section size = 1 m2
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Area = {160 + (60/2)} x 1 m2 = 190 m2
The Using of Graphical Paper (2)
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The Using of Graphical Paper (2)
Section size = 0.25 m2
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The Using of Graphical Paper (2)
717 sections
Section size = 0.25 m2
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The Using of Graphical Paper (2)
123 sections
717 sections
Section size = 0.25 m2
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The Using of Graphical Paper (2)
123 sections
717 sections
Section size = 0.25 m2
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Area = {717 + (123/2)} x 0.25 m2 = 194.6 m2
Triangle Approaching
• Use for the area which have straight side and the
amount of sides are limited
• The result is quite accurate
• The area is divided to some triangles and the area of
each triangle is calculated separately by using the
following formula:
Area = ½ a1a2 sin α3
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Triangle Approaching
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Triangle Approaching
C
A
B
D
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Triangle Approaching
a1
α3
A
a2
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Area A = ½ a1a2 sin α3
Triangle Approaching
b1
B
β3
b2
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Area B = ½ b1b2 sin β3
Triangle Approaching
c2
γ3
C
c1
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Area C = ½ c1c2 sin γ3
Triangle Approaching
D
d1
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δ3
Area D = ½ d1d2 sin δ3
Triangle Approaching
C
A
B
D
Total Area = Area A + Area B + Area C + Area D
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Coordinate Approaching
• Most suitable for calculation by machine (computer)
• The coordinates of all corner point should be available
• More accurate for the area which have sides in straight
line
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Coordinate Approaching
A (05+50, 12+80)
B (19+00, 11+30)
F (00+00, 10+50)
E (01+70, 02+00)
C (17+00, 01+40)
D (08+00, 00+00)
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Coordinate Approaching
A (05+50, 12+80)
B (19+00, 11+30)
1
F (00+00, 10+50)
2
E (01+70, 02+00)
C (17+00, 01+40)
3
D (08+00, 00+00)
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Coordinate Approaching
A (05+50, 12+80)
4
B (19+00, 11+30)
1
F (00+00, 10+50)
2
5
E (01+70, 02+00)
6
C (17+00, 01+40)
3
D (08+00, 00+00)
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Coordinate Approaching
A (05+50, 12+80)
4
B (19+00, 11+30)
1
F (00+00, 10+50)
2
5
E (01+70, 02+00)
6
C (17+00, 01+40)
3
D (08+00, 00+00)
Total Area = (Area 1 + Area 2 + Area 3) - (Area 4 + Area 5 + Area 6)
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Coordinate Approaching
A (05+50, 12+80)
B (19+00, 11+30)
1
F (00+00, 10+50)
E (01+70, 02+00)
C (17+00, 01+40)
D (08+00, 00+00)
Area 1 = ½ (5.5 + 19) (12.8 – 11.3) = 18.375
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Coordinate Approaching
A (05+50, 12+80)
B (19+00, 11+30)
F (00+00, 10+50)
2
E (01+70, 02+00)
C (17+00, 01+40)
D (08+00, 00+00)
Area 2 = ½ (19 + 17) (11.3 – 1.4) = 178.2
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Coordinate Approaching
A (05+50, 12+80)
B (19+00, 11+30)
F (00+00, 10+50)
E (01+70, 02+00)
C (17+00, 01+40)
3
D (08+00, 00+00)
Area 3 = ½ (17 + 8) (1,4 - 0) = 17.5
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Coordinate Approaching
A (05+50, 12+80)
4
B (19+00, 11+30)
F (00+00, 10+50)
E (01+70, 02+00)
C (17+00, 01+40)
D (08+00, 00+00)
Area 4 = ½ (5.5 + 0) (12.8 – 10.5) = 6.325
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Coordinate Approaching
A (05+50, 12+80)
B (19+00, 11+30)
F (00+00, 10+50)
5
E (01+70, 02+00)
C (17+00, 01+40)
D (08+00, 00+00)
Luas 5 = ½ (0 + 1.7) (10.5 - 2) = 7.225
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Coordinate Approaching
A (05+50, 12+80)
B (19+00, 11+30)
F (00+00, 10+50)
E (01+70, 02+00)
C (17+00, 01+40)
6
D (08+00, 00+00)
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Area 6 = ½ (1.7 + 8) (2 - 0) = 9.7
Coordinate Approaching
A (05+50, 12+80)
4
B (19+00, 11+30)
1
F (00+00, 10+50)
2
5
E (01+70, 02+00)
6
C (17+00, 01+40)
3
D (08+00, 00+00)
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Total Area = 190.825
Trapezoidal Approaching
• Suitable for the area which have 3 straight sides and 2 of
them is perpendicular to the third side.
• The other sides are assumed be able to approach as
straight line
• The measurement area is divided to several parts which
have same width
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Trapezoidal Approaching
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Trapezoidal Approaching
h1
h2
d
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h3
d
h4
d
h5
d
h6
d
h7
d
h8
d
Area = d {(h1 + hn)/2 + h2 + h3 + … + hn-1}
Simpson Approaching
• Suitable for the area which have 3 straight sides and 2 of them is
perpendicular to the third side.
• The measurement area is divided to several parts which have same
width
• The formula is only valid if the amount of parts is even
• In case of the number of parts is odd, the first part or the last part is
measured separately as a trapezoidal
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Simpson Approaching
h1
h2
d
h3
d
h4
d
h5
d
h6
d
h7
d
h8
d
Area = d/3 {(h1 + hn) + 2 (h3 + h5 + … + hn-2) + 4 (h2 + h4 + … + hn-1)}
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Planimeter
• Can be used to measure the area of irregular shape.
• Accurate.
• The area can be read directly in defined scale.
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