1.Obliczanie stałej C₁

Wzór:

$$C_{1} = \frac{P}{n_{Sr}}$$

Wyniki planimetrowania wzorcowego kwadratu w skali 1:1500

1. 4326

1002

1. 5328

1004

1. 6332

1002

1. 7334

$$n_{Sr} = \frac{1002 + 1004 + 1002}{3} = 1002,67$$

Powierzchnia w terenie:

P =  p * M²

Gdzie :

p- powierzchnia na mapie

M- mianownik skali

Skala : 1:1500

P =  100m² * 1500² =  225′000′000cm² =  22′500m²

Stała C₁:

$$C_{1} = \ \frac{P}{n_{Sr}}$$

$$C_{1} = \ \frac{22'500m^{2}}{1002,67} = 22,44m^{2}$$

2.Obliczanie danej powierzchni:

1. 2257

809

1. 3066

812

1. 3878

810

$$n_{Sr} = \frac{809 + 812 + 810}{3} = 810,33$$

Powierzchnia w terenie:

P =  C₁ *  n_Sr  

P =  22, 44 m²* 810, 33=18183, 80 m²

3.Metoda Graficzna

$$\text{P\ }_{\Delta} = \ \frac{a\ *h\ }{2}$$

$$P_{1}^{I} = \ \frac{\ 10,1*44}{2} = \ 22,22\text{cm}^{2}$$

$$P_{2}^{I} = \ \frac{13,6*\ 2,05}{2} = \ 13,94\text{cm}^{2}$$

$$P_{3}^{I} = \ \frac{13,6*\ 4,1}{2} = \ 27,88\text{cm}^{2}$$

$$P_{4}^{I} = \frac{11*\ 3,1}{2} = \ 17,05\text{cm}^{2}$$

P_c^I =  P₁^I + P₂^I + P₃^I + P₄^I

P_c^I= 81, 09cm² 

$$P_{1}^{\text{II}} = \ \frac{\ 10,1*44}{2} = \ 22,22\text{cm}^{2}$$

$$P_{2}^{II} = \ \frac{8,8*\ 7,25}{2} = \ 31,9\text{cm}^{2}$$

$$P_{3}^{II} = \ \frac{8,8*3,6}{2} = \ 15,84\text{cm}^{2}$$

$$P_{4}^{\text{II}} = \frac{4,2*5,3}{2} = \ 11,13\text{cm}^{2}$$

P_c^II =  P₁^II + P₂^II + P₃^II + P₄^II

P_c^II= 81, 09 cm²

|P_c^II−P_c^I|  ≤  0, 02 P

P =  81, 09cm²*1500²=182^′452^′500cm²=18245, 25m²

4.Metoda analityczna

$$2P = \sum_{i = 1}^{n}{x_{i}\left( y_{i + 1} - y_{i - 1} \right)}$$

2P= x₁(y₂-y₆)+x₂(y₃-y₁)+x₃(y₄-y₂)+x₄(y₅-y₃)+x₅(y₆-y₄)+x₆(y₁-y₅)

2P= 64,20(42,10+86,80)+41,30(65,9+67,6)- 33,00(40,00-42,10)-109,30(-15,40-65,90)- 78,90(-86,80-40,00)-76,40(-67,60+15,40)= 34135,58

2P=36736,92 /:2

P= 18368,46

$$- 2P = \sum_{i = 1}^{n}{y_{i}\left( x_{i + 1} - x_{i - 1} \right)}$$

-2P= y₁(x₂-x₆)+y₂(x₃-x₁)+y₃(x₄-x₂)+y₄(x₅-x₃)+y₅(x₆-x₄)+y₆(x₁-x₅)

-2P=-67,60(41,30+76,40)+42,10(-33,00-64,20)+65,90(-109,30-41,30)+40,00(-78,90+33,00)-15,40(-76,4+109,30)-86,8(64,20+78,90)=-36736,92

-2P=-36736,92 /: (-2)

P= 18368,46