Centroid of a composite area: rectangles and triangles

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William Haynes

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Question statement

{applet()}

Determine the coordinates of the centroid of the polygon shown. Grid units are [{units}].

Consider the polygon to be made up of a ({b0} $\times$ {h0}) rectangle {sign1} a ({b1} $\times$ {h1}) triangle {sign2} a ({b2} $\times$ {h2}) triangle.

Give any introductory information the student needs.

			Name	Type	Generated Value

b0	quantity	quantity(11, "cm")
h0	quantity	quantity(12, "cm")
b2	quantity	quantity(11, "cm")
h1	quantity	quantity(12, "cm")
b1	quantity	quantity(7, "cm")
h2	quantity	quantity(7, "cm")
sign1	string	–
sign2	string	–
A0	quantity	quantity(132, "cm^2")
A1	quantity	quantity(-42, "cm^2")
A2	quantity	quantity(-38.5, "cm^2")
AT	quantity	quantity(51.5, "cm^2")
C0	vector	vector(5.5,6)
C2	vector	Vector with 2 components
C1	vector	vector(8.6666666667,4)

			Name	Type	Generated Value

			xbar	quantity	quantity(4.288025889967637834951456310679611650485, "cm")
			ybar	quantity	quantity(4.889967637540453572815533980582524271845, "cm")

			Name	Type	Generated Value

A	vector	vector(0,5)
B	vector	vector(11,12)
C	vector	vector(4,0)
D	vector	vector(0,0)
units	string	cm
debug	boolean	false

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
qty(B[0
  ],units)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `quantity`

quantity(11, "cm")

← Depends on:

B
units

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Info Table Gap-fill
Results Gap-fill
1. Gap $\bar{x}$ Engineering Accuracy with units
  Add
2. Gap $\bar{y}$ Engineering Accuracy with units
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Part	$A_i$	$\bar{x}_i$	$\bar{y}_i$	$A_i\bar{x}_i$	$A_i\bar{y}_i$
Rectangle	A_0	x_0	y_0	Q_{y_0}	Q_{x_0}
Triangle 1	A_1	x_1	y_1	Q_{y_1}	Q_{x_1}
Triangle 2	A_2	x_2	y_2	Q_{y_2}	Q_{x_2}
$\Sigma$	$A$			$Q_y$	$Q_x$

Advice

Part	$A_i$	$\bar{x}_i$	$\bar{y}_i$	$A_i\bar{x}_i$	$A_i\bar{y}_i$
Rectangle	{A0}	{bar(C0[0])}	{bar(C0[1])}	{Q(a0, c0[0])}	{Q(a0, c0[1])}
Triangle 1	{A1}	{bar(C1[0])}	{bar(C1[1])}	{Q(a1, c1[0])}	{Q(a1, c1[1])}
Triangle 2	{A2}	{bar(C2[0])}	{bar(C2[1])}	{Q(a2, c2[0])}	{Q(a2, c2[1])}
$\Sigma$	{AT}			{display(xbar AT)}	{display(ybar AT)}

$\qquad\bar{x} = \dfrac{\Sigma A_i\bar{x}_i}{\Sigma A_i} = \var{display(xbar)}$

$\qquad \bar{y} = \dfrac{\Sigma A_i\bar{y}_i}{\Sigma A_i} =\var{display(ybar)}$

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
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Engineering Accuracy with units		Hasn't run yet
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Engineering Accuracy with units		Hasn't run yet
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Engineering Accuracy with units		Hasn't run yet
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Engineering Accuracy with units		Hasn't run yet
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Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
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Gap-fill
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Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet

This question is used in the following exams:

Chapter 7 Exercises by William Haynes in Engineering Statics.
Chapter 07 Exercises by Michael Proudman in Engineering Statics.
19. Centroids by Composite Area by Michael Proudman in Engineering Statics.
Week 2 - Exercise - Centroids by Robert Birch in Robert's workspace.
19. Centroids by Composite Area by William Haynes in Engineering Statics.

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Centroid of a composite area: rectangles and triangles

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

William Haynes 4 years, 2 months ago

William Haynes 4 years, 2 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 6 years, 4 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `quantity`

Parts

Gap-fill

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Error

Centroid of a composite area: rectangles and triangles

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 2 months ago

William Haynes 4 years, 2 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 6 years, 4 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: quantity

Parts

Gap-fill

Generated value: `quantity`