How to compute center of gravity of trapezoid
Hot to compute the mediana / center of gravity of trapezoid in analytical geometry?
Greetings from Poland!
geometry
edited Nov 28 '18 at 2:17
Rócherz
2,7762721
asked Nov 28 '18 at 2:15
DaveG
11
add a comment |
Hot to compute the mediana / center of gravity of trapezoid in analytical geometry?
Greetings from Poland!
geometry
edited Nov 28 '18 at 2:17
Rócherz
2,7762721
asked Nov 28 '18 at 2:15
DaveG
11
30;1? Is the 1 correct?
– Elsa
Nov 28 '18 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 '18 at 4:08
add a comment |
Hot to compute the mediana / center of gravity of trapezoid in analytical geometry?
Greetings from Poland!
geometry
edited Nov 28 '18 at 2:17
Rócherz
2,7762721
asked Nov 28 '18 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 '18 at 2:17
Rócherz
2,7762721
asked Nov 28 '18 at 2:15
DaveG
11
edited Nov 28 '18 at 2:17
Rócherz
2,7762721
asked Nov 28 '18 at 2:15
DaveG
11
edited Nov 28 '18 at 2:17
Rócherz
2,7762721
edited Nov 28 '18 at 2:17
Rócherz
2,7762721
edited Nov 28 '18 at 2:17
Rócherz
2,7762721
2,7762721
asked Nov 28 '18 at 2:15
DaveG
11
asked Nov 28 '18 at 2:15
DaveG
11
asked Nov 28 '18 at 2:15
DaveG
11
11
30;1? Is the 1 correct?
– Elsa
Nov 28 '18 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 '18 at 4:08
add a comment |
30;1? Is the 1 correct?
– Elsa
Nov 28 '18 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 '18 at 4:08
30;1? Is the 1 correct?
– Elsa
Nov 28 '18 at 2:52
30;1? Is the 1 correct?
– Elsa
Nov 28 '18 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 '18 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 '18 at 4:08
add a comment |
1 Answer
1
active
oldest
votes
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 '18 at 2:44
3684
1277
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3016611%2fhow-to-compute-center-of-gravity-of-trapezoid%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 '18 at 2:44
3684
1277
add a comment |
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 '18 at 2:44
3684
1277
add a comment |
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 '18 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 '18 at 2:44
3684
1277
answered Nov 28 '18 at 2:44
3684
1277
answered Nov 28 '18 at 2:44
3684
1277
answered Nov 28 '18 at 2:44
3684
1277
1277
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3016611%2fhow-to-compute-center-of-gravity-of-trapezoid%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
30;1? Is the 1 correct?
– Elsa
Nov 28 '18 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 '18 at 4:08