How to compute center of gravity of trapezoid
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Hot to compute the mediana / center of gravity of trapezoid in analytical geometry?
Greetings from Poland!
geometry
edited Nov 28 at 2:17
Rócherz
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asked Nov 28 at 2:15
DaveG
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up vote
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Hot to compute the mediana / center of gravity of trapezoid in analytical geometry?
Greetings from Poland!
geometry
edited Nov 28 at 2:17
Rócherz
2,7412721
asked Nov 28 at 2:15
DaveG
11
30;1? Is the 1 correct?
– Elsa
Nov 28 at 2:52
Quoting wiki's entry of centroid of a polygon, $$ begin{align} C_x &= frac{1}{6A} sum_{i=0}^{n-1}(x_i + x_{i+1})(x_i y_{i+1} - x_{i+1}y_i)\ C_y &= frac{1}{6A} sum_{i=0}^{n-1}(y_i + y_{i+1})(x_i y_{i+1} - x_{i+1}y_i) end{align} $$ where $A = frac12sumlimits_{i=0}^{n-1}(x_i y_{i+1} - x_{i+1}y_i)$ is polygon's signed area.
– achille hui
Nov 28 at 4:08
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0
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favorite
up vote
0
down vote
favorite
Hot to compute the mediana / center of gravity of trapezoid in analytical geometry?
Greetings from Poland!
geometry
edited Nov 28 at 2:17
Rócherz
2,7412721
asked Nov 28 at 2:15
DaveG
11
Hot to compute the mediana / center of gravity of trapezoid in analytical geometry?
Greetings from Poland!
geometry
geometry
edited Nov 28 at 2:17
Rócherz
2,7412721
asked Nov 28 at 2:15
DaveG
11
edited Nov 28 at 2:17
Rócherz
2,7412721
asked Nov 28 at 2:15
DaveG
11
edited Nov 28 at 2:17
Rócherz
2,7412721
edited Nov 28 at 2:17
Rócherz
2,7412721
edited Nov 28 at 2:17
Rócherz
2,7412721
2,7412721
asked Nov 28 at 2:15
DaveG
11
asked Nov 28 at 2:15
DaveG
11
asked Nov 28 at 2:15
DaveG
11
11
30;1? Is the 1 correct?
– Elsa
Nov 28 at 2:52
Quoting wiki's entry of centroid of a polygon, $$ begin{align} C_x &= frac{1}{6A} sum_{i=0}^{n-1}(x_i + x_{i+1})(x_i y_{i+1} - x_{i+1}y_i)\ C_y &= frac{1}{6A} sum_{i=0}^{n-1}(y_i + y_{i+1})(x_i y_{i+1} - x_{i+1}y_i) end{align} $$ where $A = frac12sumlimits_{i=0}^{n-1}(x_i y_{i+1} - x_{i+1}y_i)$ is polygon's signed area.
– achille hui
Nov 28 at 4:08
add a comment |
30;1? Is the 1 correct?
– Elsa
Nov 28 at 2:52
Quoting wiki's entry of centroid of a polygon, $$ begin{align} C_x &= frac{1}{6A} sum_{i=0}^{n-1}(x_i + x_{i+1})(x_i y_{i+1} - x_{i+1}y_i)\ C_y &= frac{1}{6A} sum_{i=0}^{n-1}(y_i + y_{i+1})(x_i y_{i+1} - x_{i+1}y_i) end{align} $$ where $A = frac12sumlimits_{i=0}^{n-1}(x_i y_{i+1} - x_{i+1}y_i)$ is polygon's signed area.
– achille hui
Nov 28 at 4:08
30;1? Is the 1 correct?
– Elsa
Nov 28 at 2:52
30;1? Is the 1 correct?
– Elsa
Nov 28 at 2:52
Quoting wiki's entry of centroid of a polygon, $$ begin{align} C_x &= frac{1}{6A} sum_{i=0}^{n-1}(x_i + x_{i+1})(x_i y_{i+1} - x_{i+1}y_i)\ C_y &= frac{1}{6A} sum_{i=0}^{n-1}(y_i + y_{i+1})(x_i y_{i+1} - x_{i+1}y_i) end{align} $$ where $A = frac12sumlimits_{i=0}^{n-1}(x_i y_{i+1} - x_{i+1}y_i)$ is polygon's signed area.
– achille hui
Nov 28 at 4:08
Quoting wiki's entry of centroid of a polygon, $$ begin{align} C_x &= frac{1}{6A} sum_{i=0}^{n-1}(x_i + x_{i+1})(x_i y_{i+1} - x_{i+1}y_i)\ C_y &= frac{1}{6A} sum_{i=0}^{n-1}(y_i + y_{i+1})(x_i y_{i+1} - x_{i+1}y_i) end{align} $$ where $A = frac12sumlimits_{i=0}^{n-1}(x_i y_{i+1} - x_{i+1}y_i)$ is polygon's signed area.
– achille hui
Nov 28 at 4:08
add a comment |
1 Answer
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Hint: break the shape into two parts and take moments about a point. I am happy to provide a full solution if you still need help.
answered Nov 28 at 2:44
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Hint: break the shape into two parts and take moments about a point. I am happy to provide a full solution if you still need help.
answered Nov 28 at 2:44
3684
1277
add a comment |
up vote
0
down vote
Hint: break the shape into two parts and take moments about a point. I am happy to provide a full solution if you still need help.
answered Nov 28 at 2:44
3684
1277
add a comment |
up vote
0
down vote
up vote
0
down vote
Hint: break the shape into two parts and take moments about a point. I am happy to provide a full solution if you still need help.
answered Nov 28 at 2:44
3684
1277
Hint: break the shape into two parts and take moments about a point. I am happy to provide a full solution if you still need help.
answered Nov 28 at 2:44
3684
1277
answered Nov 28 at 2:44
3684
1277
answered Nov 28 at 2:44
3684
1277
answered Nov 28 at 2:44
3684
1277
1277
add a comment |
add a comment |
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30;1? Is the 1 correct?
– Elsa
Nov 28 at 2:52
Quoting wiki's entry of centroid of a polygon, $$ begin{align} C_x &= frac{1}{6A} sum_{i=0}^{n-1}(x_i + x_{i+1})(x_i y_{i+1} - x_{i+1}y_i)\ C_y &= frac{1}{6A} sum_{i=0}^{n-1}(y_i + y_{i+1})(x_i y_{i+1} - x_{i+1}y_i) end{align} $$ where $A = frac12sumlimits_{i=0}^{n-1}(x_i y_{i+1} - x_{i+1}y_i)$ is polygon's signed area.
– achille hui
Nov 28 at 4:08