The area of all the points within the set defined as…

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Let $C$ be a set in two dimensions and let $Q(C)$ be the area of $C$ if $C$ has a finite area; otherwise let $Q(C)$ be undefined.



So if we have this set, the book says,



$$C = (x,y): 0 leq x, 0 leq y, x+yleq1$$



$Q(C) = frac12$



I'm struggling to have the ideas or concepts in my head to easily establish or see that the area is 1/2.
Can anybody help?




geometry




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  • 2




    Have you drawn a diagram?
    – N. F. Taussig
    Aug 23 at 9:27






  • 2




    You are essentially asked to determine the area of a triangle that is defined by 3 inequalities in 2D euclidean space. Draw the triangle, calculate its area and you are done
    – Aleksejs Fomins
    Aug 23 at 10:49










  • Oh yeah, sorry, I see where I went wrong. Yes I did draw a diagram, but I forgot one thing, that x and y are constrained to the 1st quadrant. Thanks.
    – Bucephalus
    Aug 23 at 11:03










  • Can you put that answer up @AleksejsFomins so I can close the question out. Thanks.
    – Bucephalus
    Aug 23 at 11:05










  • Thanks @N.F.Taussig too.
    – Bucephalus
    Aug 23 at 11:05














up vote
0
down vote

favorite












Let $C$ be a set in two dimensions and let $Q(C)$ be the area of $C$ if $C$ has a finite area; otherwise let $Q(C)$ be undefined.



So if we have this set, the book says,



$$C = (x,y): 0 leq x, 0 leq y, x+yleq1$$



$Q(C) = frac12$



I'm struggling to have the ideas or concepts in my head to easily establish or see that the area is 1/2.
Can anybody help?




geometry




share|cite|improve this question


















  • 2




    Have you drawn a diagram?
    – N. F. Taussig
    Aug 23 at 9:27






  • 2




    You are essentially asked to determine the area of a triangle that is defined by 3 inequalities in 2D euclidean space. Draw the triangle, calculate its area and you are done
    – Aleksejs Fomins
    Aug 23 at 10:49










  • Oh yeah, sorry, I see where I went wrong. Yes I did draw a diagram, but I forgot one thing, that x and y are constrained to the 1st quadrant. Thanks.
    – Bucephalus
    Aug 23 at 11:03










  • Can you put that answer up @AleksejsFomins so I can close the question out. Thanks.
    – Bucephalus
    Aug 23 at 11:05










  • Thanks @N.F.Taussig too.
    – Bucephalus
    Aug 23 at 11:05












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let $C$ be a set in two dimensions and let $Q(C)$ be the area of $C$ if $C$ has a finite area; otherwise let $Q(C)$ be undefined.



So if we have this set, the book says,



$$C = (x,y): 0 leq x, 0 leq y, x+yleq1$$



$Q(C) = frac12$



I'm struggling to have the ideas or concepts in my head to easily establish or see that the area is 1/2.
Can anybody help?




geometry




share|cite|improve this question














Let $C$ be a set in two dimensions and let $Q(C)$ be the area of $C$ if $C$ has a finite area; otherwise let $Q(C)$ be undefined.



So if we have this set, the book says,



$$C = (x,y): 0 leq x, 0 leq y, x+yleq1$$



$Q(C) = frac12$



I'm struggling to have the ideas or concepts in my head to easily establish or see that the area is 1/2.
Can anybody help?





geometry





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 23 at 11:39









Andrés E. Caicedo

63.3k7153238




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asked Aug 23 at 9:23









Bucephalus

446214




446214







  • 2




    Have you drawn a diagram?
    – N. F. Taussig
    Aug 23 at 9:27






  • 2




    You are essentially asked to determine the area of a triangle that is defined by 3 inequalities in 2D euclidean space. Draw the triangle, calculate its area and you are done
    – Aleksejs Fomins
    Aug 23 at 10:49










  • Oh yeah, sorry, I see where I went wrong. Yes I did draw a diagram, but I forgot one thing, that x and y are constrained to the 1st quadrant. Thanks.
    – Bucephalus
    Aug 23 at 11:03










  • Can you put that answer up @AleksejsFomins so I can close the question out. Thanks.
    – Bucephalus
    Aug 23 at 11:05










  • Thanks @N.F.Taussig too.
    – Bucephalus
    Aug 23 at 11:05












  • 2




    Have you drawn a diagram?
    – N. F. Taussig
    Aug 23 at 9:27






  • 2




    You are essentially asked to determine the area of a triangle that is defined by 3 inequalities in 2D euclidean space. Draw the triangle, calculate its area and you are done
    – Aleksejs Fomins
    Aug 23 at 10:49










  • Oh yeah, sorry, I see where I went wrong. Yes I did draw a diagram, but I forgot one thing, that x and y are constrained to the 1st quadrant. Thanks.
    – Bucephalus
    Aug 23 at 11:03










  • Can you put that answer up @AleksejsFomins so I can close the question out. Thanks.
    – Bucephalus
    Aug 23 at 11:05










  • Thanks @N.F.Taussig too.
    – Bucephalus
    Aug 23 at 11:05







2




2




Have you drawn a diagram?
– N. F. Taussig
Aug 23 at 9:27




Have you drawn a diagram?
– N. F. Taussig
Aug 23 at 9:27




2




2




You are essentially asked to determine the area of a triangle that is defined by 3 inequalities in 2D euclidean space. Draw the triangle, calculate its area and you are done
– Aleksejs Fomins
Aug 23 at 10:49




You are essentially asked to determine the area of a triangle that is defined by 3 inequalities in 2D euclidean space. Draw the triangle, calculate its area and you are done
– Aleksejs Fomins
Aug 23 at 10:49












Oh yeah, sorry, I see where I went wrong. Yes I did draw a diagram, but I forgot one thing, that x and y are constrained to the 1st quadrant. Thanks.
– Bucephalus
Aug 23 at 11:03




Oh yeah, sorry, I see where I went wrong. Yes I did draw a diagram, but I forgot one thing, that x and y are constrained to the 1st quadrant. Thanks.
– Bucephalus
Aug 23 at 11:03












Can you put that answer up @AleksejsFomins so I can close the question out. Thanks.
– Bucephalus
Aug 23 at 11:05




Can you put that answer up @AleksejsFomins so I can close the question out. Thanks.
– Bucephalus
Aug 23 at 11:05












Thanks @N.F.Taussig too.
– Bucephalus
Aug 23 at 11:05




Thanks @N.F.Taussig too.
– Bucephalus
Aug 23 at 11:05










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You are essentially asked to determine the area of a triangle that is defined by 3 linear inequalities in a 2D euclidean space. Draw 3 lines, color the half-spaces corresponding to the inequalities, the intersection of all 3 will be a triangle. Calculate its area and you are done






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    1 Answer
    1






    active

    oldest

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    oldest

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    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    You are essentially asked to determine the area of a triangle that is defined by 3 linear inequalities in a 2D euclidean space. Draw 3 lines, color the half-spaces corresponding to the inequalities, the intersection of all 3 will be a triangle. Calculate its area and you are done






    share|cite|improve this answer
























      up vote
      1
      down vote



      accepted










      You are essentially asked to determine the area of a triangle that is defined by 3 linear inequalities in a 2D euclidean space. Draw 3 lines, color the half-spaces corresponding to the inequalities, the intersection of all 3 will be a triangle. Calculate its area and you are done






      share|cite|improve this answer






















        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        You are essentially asked to determine the area of a triangle that is defined by 3 linear inequalities in a 2D euclidean space. Draw 3 lines, color the half-spaces corresponding to the inequalities, the intersection of all 3 will be a triangle. Calculate its area and you are done






        share|cite|improve this answer












        You are essentially asked to determine the area of a triangle that is defined by 3 linear inequalities in a 2D euclidean space. Draw 3 lines, color the half-spaces corresponding to the inequalities, the intersection of all 3 will be a triangle. Calculate its area and you are done







        share|cite|improve this answer












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        answered Aug 23 at 11:07









        Aleksejs Fomins

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