1. E4004 Surveying Computations A Area Problems

2. To Cut Off an Area by a Line Passing Through a Fixed Point The bearing and distance BP is known B P X Brg Dist Brg The bearing BX is known The required area BPX is known Calculate the bearing and distance PX and the distance BX

3. To Cut Off an Area by a Line Passing Through a Fixed Point The angle at B is determined from the bearing difference B P X Brg Dist Brg The general formula for the area of a triangle is C B A a b

4. To Cut Off an Area by a Line Passing Through a Fixed Point The bearing & distance of the line PX can be calculated by closing PBX B P X Brg Dist Brg Also check that the area PBX calculates to the correct area by using the CLOSE program

5. To Cut Off an Area by a Line Passing Through a Particular Point A farmer wants to fence off a particular area from a large paddock.There is an existing trough which must be accessible to stock on both sides of the new fence.

6. To Cut Off an Area by a Line Passing Through a Particular Point The bearings of BC and BD are known. B C D Brg The bearing and distance BP can be measured. Brg Dist P The required area is  A

7. To Cut Off an Area by a Line Passing Through a Particular Point Note that there will be two solutions B C D Brg Dist P Such that C’ D’

8. To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y   Let

9. To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y  

10. To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y   Multiply both sides of the equation by, x sin(  ) Re-write in terms of x

11. To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y   This equation is in quadratic form and can be solved for x Make the LHS equal zero

12. To Cut Off an Area by a Line Passing Through a Particular Point Write a program to solve for x in a quadratic given values for a, b and c OR write a solver program which will solve for x, a, b or c

13. To Cut Off an Area by a Line Passing Through a Particular Point When the Figure is not a Triangle It is required to cut off a given area CQRSTD by a line passing through P C Q R S T D P The bearings and distances QR, RS and ST are known whilst the position of P has been located from Q Brg & Dist Only the bearings are known for CQ and TD Brg AA

14. To Cut Off an Area by a Line Passing Through a Particular Point When the Figure is not a Triangle Extend CQ and DT to intersect at B C Q R S T D P The figure CBDF is the same as that formed in the earlier example provided the required area is made equal to the sum of Area QRSTB and  A Brg & Dist Brg B AA The dimensions of lines TB and BQ can be calculated by closing QRSTB and the line BP by closing BQP