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Session 9 AREA MEASUREMENT Course: S0663 – Land Surveying Year: 2007

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Bina Nusantara Area Measurement Methods Graphical Measurement Analytical Measurement Measurement using Area Measuring Apparatus

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Bina Nusantara 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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Bina Nusantara 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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Bina Nusantara The Using of Graphical Paper (1)

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Bina Nusantara The Using of Graphical Paper (1) Section size = 1 m 2

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Bina Nusantara The Using of Graphical Paper (1) Section size = 1 m 2 160 sections

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Bina Nusantara The Using of Graphical Paper (1) Section size = 1 m 2 160 sections 60 sections

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Bina Nusantara The Using of Graphical Paper (1) Section size = 1 m 2 160 sections 60 sections Area = {160 + (60/2)} x 1 m 2 = 190 m 2

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Bina Nusantara The Using of Graphical Paper (2)

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Bina Nusantara The Using of Graphical Paper (2) Section size = 0.25 m 2

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Bina Nusantara The Using of Graphical Paper (2) Section size = 0.25 m 2 717 sections

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Bina Nusantara The Using of Graphical Paper (2) Section size = 0.25 m 2 717 sections 123 sections

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Bina Nusantara The Using of Graphical Paper (2) Section size = 0.25 m 2 717 sections 123 sections Area = {717 + (123/2)} x 0.25 m 2 = 194.6 m 2

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Bina Nusantara 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 a 1 a 2 sin α 3

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Bina Nusantara Triangle Approaching

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Bina Nusantara Triangle Approaching A B C D

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Bina Nusantara Triangle Approaching A a1a1a1a1 a2a2a2a2 α3α3α3α3 Area A = ½ a 1 a 2 sin α 3

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Bina Nusantara Triangle Approaching B b1b1b1b1 b2b2b2b2 β3β3β3β3 Area B = ½ b 1 b 2 sin β 3

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Bina Nusantara Triangle Approaching C c2c2c2c2 c1c1c1c1 γ3γ3γ3γ3 Area C = ½ c 1 c 2 sin γ 3

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Bina Nusantara Triangle Approaching D d2d2d2d2 d1d1d1d1 δ3δ3δ3δ3 Area D = ½ d 1 d 2 sin δ 3

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Bina Nusantara Triangle Approaching A B C D Total Area = Area A + Area B + Area C + Area D

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Bina Nusantara 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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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50)

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 1 2 3

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 1 2 3 4 5 6

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 1 2 3 4 5 6 Total Area = (Area 1 + Area 2 + Area 3) - (Area 4 + Area 5 + Area 6)

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 1 Area 1 = ½ (5.5 + 19) (12.8 – 11.3) = 18.375

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 2 Area 2 = ½ (19 + 17) (11.3 – 1.4) = 178.2

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 3 Area 3 = ½ (17 + 8) (1,4 - 0) = 17.5

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 4 Area 4 = ½ (5.5 + 0) (12.8 – 10.5) = 6.325

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 5 Luas 5 = ½ (0 + 1.7) (10.5 - 2) = 7.225

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 6 Area 6 = ½ (1.7 + 8) (2 - 0) = 9.7

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Bina Nusantara Coordinate Approaching A (05+50, 12+80) B (19+00, 11+30) C (17+00, 01+40) D (08+00, 00+00) E (01+70, 02+00) F (00+00, 10+50) 1 2 3 4 5 6 Total Area = 190.825

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Bina Nusantara 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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Bina Nusantara Trapezoidal Approaching

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Bina Nusantara Trapezoidal Approaching d d ddddd h1h1 h2h2 h3h3 h4h4 h5h5 h6h6 h7h7 h8h8 Area = d {(h 1 + h n )/2 + h 2 + h 3 + … + h n-1 }

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Bina Nusantara 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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Bina Nusantara Simpson Approaching Area = d/3 {(h 1 + h n ) + 2 (h 3 + h 5 + … + h n-2 ) + 4 ( h 2 + h 4 + … + h n-1 )} d d ddddd h1h1 h2h2 h3h3 h4h4 h5h5 h6h6 h7h7 h8h8

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Bina Nusantara 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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