why area of triangle changes when measured as components of triangles? [closed]

0

$begingroup$

If we measure an area of triangle directly using a formula I got 90 square unit. But if we measure by components like 2 triangles and one rectangle and take some it counts 90.5

Why 0.5 square unit difference occur?

Any Help will be appreciated

geometry triangle

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edited Jan 14 at 16:21

Todd Sewell

210314

asked Jan 14 at 9:24

SRJSRJ

1,7431620

$endgroup$

closed as off-topic by user21820, Lord Shark the Unknown, Eevee Trainer, Leucippus, Xander Henderson Jan 15 at 4:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Lord Shark the Unknown, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  12
  

  
  
  
  
  
  

  
  $begingroup$
  Is this meant as a riddle? The union of the colored areas is not a triangle.
  $endgroup$
  – Martin R
  Jan 14 at 9:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes.I wanted to know why such thing is happening
  $endgroup$
  – SRJ
  Jan 14 at 9:33
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Related: How come $32.5 = 31.5$? (The “Missing Square” puzzle.)
  $endgroup$
  – Andrew T.
  Jan 14 at 16:19
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  See the addendum to THIS ANSWER
  $endgroup$
  – steven gregory
  Jan 14 at 21:38
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

If we measure an area of triangle directly using a formula I got 90 square unit. But if we measure by components like 2 triangles and one rectangle and take some it counts 90.5

Why 0.5 square unit difference occur?

Any Help will be appreciated

geometry triangle

share|cite|improve this question

edited Jan 14 at 16:21

Todd Sewell

210314

asked Jan 14 at 9:24

SRJSRJ

1,7431620

$endgroup$

closed as off-topic by user21820, Lord Shark the Unknown, Eevee Trainer, Leucippus, Xander Henderson Jan 15 at 4:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Lord Shark the Unknown, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  12
  

  
  
  
  
  
  

  
  $begingroup$
  Is this meant as a riddle? The union of the colored areas is not a triangle.
  $endgroup$
  – Martin R
  Jan 14 at 9:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes.I wanted to know why such thing is happening
  $endgroup$
  – SRJ
  Jan 14 at 9:33
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Related: How come $32.5 = 31.5$? (The “Missing Square” puzzle.)
  $endgroup$
  – Andrew T.
  Jan 14 at 16:19
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  See the addendum to THIS ANSWER
  $endgroup$
  – steven gregory
  Jan 14 at 21:38
  
  
  

  
  
  
  

add a comment | 

0

0

0

1

$begingroup$

If we measure an area of triangle directly using a formula I got 90 square unit. But if we measure by components like 2 triangles and one rectangle and take some it counts 90.5

Why 0.5 square unit difference occur?

Any Help will be appreciated

geometry triangle

share|cite|improve this question

edited Jan 14 at 16:21

Todd Sewell

210314

asked Jan 14 at 9:24

SRJSRJ

1,7431620

$endgroup$

If we measure an area of triangle directly using a formula I got 90 square unit. But if we measure by components like 2 triangles and one rectangle and take some it counts 90.5

Why 0.5 square unit difference occur?

Any Help will be appreciated

geometry triangle

geometry triangle

share|cite|improve this question

edited Jan 14 at 16:21

Todd Sewell

210314

asked Jan 14 at 9:24

SRJSRJ

1,7431620

share|cite|improve this question

edited Jan 14 at 16:21

Todd Sewell

210314

asked Jan 14 at 9:24

SRJSRJ

1,7431620

share|cite|improve this question

share|cite|improve this question

edited Jan 14 at 16:21

Todd Sewell

210314

edited Jan 14 at 16:21

Todd Sewell

210314

edited Jan 14 at 16:21

Todd Sewell

210314

210314

asked Jan 14 at 9:24

SRJSRJ

1,7431620

asked Jan 14 at 9:24

SRJSRJ

1,7431620

asked Jan 14 at 9:24

SRJSRJ

1,7431620

1,7431620

closed as off-topic by user21820, Lord Shark the Unknown, Eevee Trainer, Leucippus, Xander Henderson Jan 15 at 4:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Lord Shark the Unknown, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by user21820, Lord Shark the Unknown, Eevee Trainer, Leucippus, Xander Henderson Jan 15 at 4:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Lord Shark the Unknown, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  12
  

  
  
  
  
  
  

  
  $begingroup$
  Is this meant as a riddle? The union of the colored areas is not a triangle.
  $endgroup$
  – Martin R
  Jan 14 at 9:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes.I wanted to know why such thing is happening
  $endgroup$
  – SRJ
  Jan 14 at 9:33
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Related: How come $32.5 = 31.5$? (The “Missing Square” puzzle.)
  $endgroup$
  – Andrew T.
  Jan 14 at 16:19
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  See the addendum to THIS ANSWER
  $endgroup$
  – steven gregory
  Jan 14 at 21:38
  
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  12
  

  
  
  
  
  
  

  
  $begingroup$
  Is this meant as a riddle? The union of the colored areas is not a triangle.
  $endgroup$
  – Martin R
  Jan 14 at 9:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes.I wanted to know why such thing is happening
  $endgroup$
  – SRJ
  Jan 14 at 9:33
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Related: How come $32.5 = 31.5$? (The “Missing Square” puzzle.)
  $endgroup$
  – Andrew T.
  Jan 14 at 16:19
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  See the addendum to THIS ANSWER
  $endgroup$
  – steven gregory
  Jan 14 at 21:38
  
  
  

  
  
  
  

12

12

$begingroup$
Is this meant as a riddle? The union of the colored areas is not a triangle.
$endgroup$
– Martin R
Jan 14 at 9:31

$begingroup$
Is this meant as a riddle? The union of the colored areas is not a triangle.
$endgroup$
– Martin R
Jan 14 at 9:31

$begingroup$
yes.I wanted to know why such thing is happening
$endgroup$
– SRJ
Jan 14 at 9:33

$begingroup$
yes.I wanted to know why such thing is happening
$endgroup$
– SRJ
Jan 14 at 9:33

2

2

$begingroup$
Related: How come $32.5 = 31.5$? (The “Missing Square” puzzle.)
$endgroup$
– Andrew T.
Jan 14 at 16:19

$begingroup$
Related: How come $32.5 = 31.5$? (The “Missing Square” puzzle.)
$endgroup$
– Andrew T.
Jan 14 at 16:19

$begingroup$
See the addendum to THIS ANSWER
$endgroup$
– steven gregory
Jan 14 at 21:38

$begingroup$
See the addendum to THIS ANSWER
$endgroup$
– steven gregory
Jan 14 at 21:38

add a comment | 

3 Answers
3

active

oldest

votes

12

$begingroup$

Because the joint point of the two segments is not on the point of $(11,5)$. As the equation of the line is $y = frac{9}{20} x$, hence the coordinate of the joint point is $(frac{20times 5}{9} = frac{100}{9}, 5)$ which is not exactly $(11,5)$.

share|cite|improve this answer

answered Jan 14 at 9:28

OmGOmG

2,512822

$endgroup$

add a comment | 

9

$begingroup$

This picture is basically what happens here.

The difference is that your picture tries to make the slope of the orange and the blue triangles almost the same as the big one, hence giving the illusion of them being sub-triangles.

share|cite|improve this answer

edited Jan 15 at 7:02

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

$endgroup$

add a comment | 

8

$begingroup$

The points A$(0,0)$ , P$(11,5)$ and B$(20,9)$ are not on the same straight line. It forms a very small triangle (APB). So, the half area of the rectangle is not the sum of the colored pieces.

$a=AP=sqrt{11^2+5^2}quad;quad b=PB=sqrt{11^2+4^2}quad;quad c=AB=sqrt{9^2+20^2}$

The calculus of the area of triangle (APB) is easy thanks to the Heron's formula :

$frac14sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}=0.5$

Similar fake problem with solution on page 23 in https://fr.scribd.com/doc/15493868/Pastiches-Paradoxes-Sophismes

share|cite|improve this answer

edited Jan 14 at 15:00

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

$endgroup$

add a comment | 

3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

12

$begingroup$

Because the joint point of the two segments is not on the point of $(11,5)$. As the equation of the line is $y = frac{9}{20} x$, hence the coordinate of the joint point is $(frac{20times 5}{9} = frac{100}{9}, 5)$ which is not exactly $(11,5)$.

share|cite|improve this answer

answered Jan 14 at 9:28

OmGOmG

2,512822

$endgroup$

add a comment | 

12

$begingroup$

Because the joint point of the two segments is not on the point of $(11,5)$. As the equation of the line is $y = frac{9}{20} x$, hence the coordinate of the joint point is $(frac{20times 5}{9} = frac{100}{9}, 5)$ which is not exactly $(11,5)$.

share|cite|improve this answer

answered Jan 14 at 9:28

OmGOmG

2,512822

$endgroup$

add a comment | 

12

12

12

$begingroup$

Because the joint point of the two segments is not on the point of $(11,5)$. As the equation of the line is $y = frac{9}{20} x$, hence the coordinate of the joint point is $(frac{20times 5}{9} = frac{100}{9}, 5)$ which is not exactly $(11,5)$.

share|cite|improve this answer

answered Jan 14 at 9:28

OmGOmG

2,512822

$endgroup$

Because the joint point of the two segments is not on the point of $(11,5)$. As the equation of the line is $y = frac{9}{20} x$, hence the coordinate of the joint point is $(frac{20times 5}{9} = frac{100}{9}, 5)$ which is not exactly $(11,5)$.

share|cite|improve this answer

answered Jan 14 at 9:28

OmGOmG

2,512822

share|cite|improve this answer

share|cite|improve this answer

answered Jan 14 at 9:28

OmGOmG

2,512822

answered Jan 14 at 9:28

OmGOmG

2,512822

answered Jan 14 at 9:28

OmGOmG

2,512822

2,512822

add a comment | 

add a comment | 

9

$begingroup$

This picture is basically what happens here.

The difference is that your picture tries to make the slope of the orange and the blue triangles almost the same as the big one, hence giving the illusion of them being sub-triangles.

share|cite|improve this answer

edited Jan 15 at 7:02

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

$endgroup$

add a comment | 

9

$begingroup$

This picture is basically what happens here.

The difference is that your picture tries to make the slope of the orange and the blue triangles almost the same as the big one, hence giving the illusion of them being sub-triangles.

share|cite|improve this answer

edited Jan 15 at 7:02

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

$endgroup$

add a comment | 

9

9

9

$begingroup$

This picture is basically what happens here.

The difference is that your picture tries to make the slope of the orange and the blue triangles almost the same as the big one, hence giving the illusion of them being sub-triangles.

share|cite|improve this answer

edited Jan 15 at 7:02

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

$endgroup$

This picture is basically what happens here.

The difference is that your picture tries to make the slope of the orange and the blue triangles almost the same as the big one, hence giving the illusion of them being sub-triangles.

share|cite|improve this answer

edited Jan 15 at 7:02

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

share|cite|improve this answer

share|cite|improve this answer

edited Jan 15 at 7:02

edited Jan 15 at 7:02

edited Jan 15 at 7:02

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

answered Jan 14 at 15:35

BigbearZzzBigbearZzz

8,72621652

8,72621652

add a comment | 

add a comment | 

8

$begingroup$

The points A$(0,0)$ , P$(11,5)$ and B$(20,9)$ are not on the same straight line. It forms a very small triangle (APB). So, the half area of the rectangle is not the sum of the colored pieces.

$a=AP=sqrt{11^2+5^2}quad;quad b=PB=sqrt{11^2+4^2}quad;quad c=AB=sqrt{9^2+20^2}$

The calculus of the area of triangle (APB) is easy thanks to the Heron's formula :

$frac14sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}=0.5$

Similar fake problem with solution on page 23 in https://fr.scribd.com/doc/15493868/Pastiches-Paradoxes-Sophismes

share|cite|improve this answer

edited Jan 14 at 15:00

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

$endgroup$

add a comment | 

8

$begingroup$

The points A$(0,0)$ , P$(11,5)$ and B$(20,9)$ are not on the same straight line. It forms a very small triangle (APB). So, the half area of the rectangle is not the sum of the colored pieces.

$a=AP=sqrt{11^2+5^2}quad;quad b=PB=sqrt{11^2+4^2}quad;quad c=AB=sqrt{9^2+20^2}$

The calculus of the area of triangle (APB) is easy thanks to the Heron's formula :

$frac14sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}=0.5$

Similar fake problem with solution on page 23 in https://fr.scribd.com/doc/15493868/Pastiches-Paradoxes-Sophismes

share|cite|improve this answer

edited Jan 14 at 15:00

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

$endgroup$

add a comment | 

8

8

8

$begingroup$

The points A$(0,0)$ , P$(11,5)$ and B$(20,9)$ are not on the same straight line. It forms a very small triangle (APB). So, the half area of the rectangle is not the sum of the colored pieces.

$a=AP=sqrt{11^2+5^2}quad;quad b=PB=sqrt{11^2+4^2}quad;quad c=AB=sqrt{9^2+20^2}$

The calculus of the area of triangle (APB) is easy thanks to the Heron's formula :

$frac14sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}=0.5$

Similar fake problem with solution on page 23 in https://fr.scribd.com/doc/15493868/Pastiches-Paradoxes-Sophismes

share|cite|improve this answer

edited Jan 14 at 15:00

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

$endgroup$

The points A$(0,0)$ , P$(11,5)$ and B$(20,9)$ are not on the same straight line. It forms a very small triangle (APB). So, the half area of the rectangle is not the sum of the colored pieces.

$a=AP=sqrt{11^2+5^2}quad;quad b=PB=sqrt{11^2+4^2}quad;quad c=AB=sqrt{9^2+20^2}$

The calculus of the area of triangle (APB) is easy thanks to the Heron's formula :

$frac14sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}=0.5$

Similar fake problem with solution on page 23 in https://fr.scribd.com/doc/15493868/Pastiches-Paradoxes-Sophismes

share|cite|improve this answer

edited Jan 14 at 15:00

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

share|cite|improve this answer

share|cite|improve this answer

edited Jan 14 at 15:00

edited Jan 14 at 15:00

edited Jan 14 at 15:00

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

answered Jan 14 at 9:38

JJacquelinJJacquelin

44k21853

44k21853

add a comment | 

add a comment | 

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