Calculate the areas of polygons

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From users who are members of Transition to university :

Chris Graham	said	Ready to use	7 years, 7 months ago
Aiden McCall	said	Needs to be tested	7 years, 8 months ago
Christian Lawson-Perfect	said	Has some problems	7 years, 8 months ago
Hannah Aldous	said	Has some problems	7 years, 9 months ago

History

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Chris Graham 7 years, 7 months ago

Gave some feedback: Ready to use

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Chris Graham commented 7 years, 7 months ago

I've shortened the advice, as there were lots of statements repeated, for exampe giving the formula for the area, then justifying it with a diagram, and then giving the formula again. Fixed typos and reworded the questions to remove duplication of "the following..." in the statement and parts.

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Aiden McCall 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham 7 years, 8 months ago

Gave some feedback: Has some problems

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Chris Graham commented 7 years, 8 months ago

Nice question. However, "a trapezium can be interpreted as half of a parallelogram, this is shown below", isn't really shown below. Since you have included the graphic of the parallelogram, I think that you need to be consistent, and include something along the lines of this: http://www.mathguide.com/lessons/pic-demotrapezoid.gif

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Aiden McCall 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Aiden McCall 7 years, 8 months ago

Gave some feedback: Has some problems

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Stanislav Duris commented 7 years, 8 months ago

Hey Aiden,

I haven't noticed Chris has already made this suggestion when I started fixing part a) for you so you could see how to fix other parts. I've done it, so part a) should now work. Don't forget to put everything in one line before you do the conditional visibility.

There was one problem I came across. Sometimes, even when wh00 = wh00dp was true, Numbas thought it was false. When I made wh00 round to 2 decimal places (so practically stay the same as it already was), this problem seems to have vanished so I advise doing the same for other parts. It is some kind of an error.

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Chris Graham commented 7 years, 8 months ago

Aiden, is it just the conditional visibility which doesn't work? If so you could put 2 versions of the whole equation into different blocks: one for wh00 = wh00dp and one for wh00 <> wh00dp.

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Aiden McCall 7 years, 8 months ago

Gave some feedback: Doesn't work

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Aiden McCall 7 years, 8 months ago

Gave some feedback: Has some problems

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Aiden McCall 7 years, 8 months ago

Gave some feedback: Doesn't work

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Why do I need to round my answer at all?

I agree with Vicky and Hannah's suggestions.

Restore this checkpoint

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Vicky Hall commented 7 years, 8 months ago

In parts a) and b), sometimes the answer is already an integer and doesn't need to be rounded so you end up with two identical lines in the advice. (Also, part a) doesn't round at all even when it should do so that needs to be fixed.) You can code your advice section so that certain lines only show if the solution does need to be rounded (I would speak to Lauren about it if you're not sure how as she has an example of this in one of her questions).

I have reworded part a) slightly to make it more succinct and I have also put the unit $\mathrm{m}$ into \mathrm. Have a look through the other parts and try to reword a bit more clearly. I agree with Hannah's advice:

$\text{I think you need to start the advice for each part with 'The area of a parallelogram is calculated using the formula...'}$ .

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Aiden McCall 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Hannah Aldous commented 7 years, 9 months ago

part a says round to 1 dp but only marked correct 2 dps
not sure how easy this is to do but on the trapezium diagram could you line up your values for the number on top and bottom
in part d, a + b needs to be in LaTeX
in your advice you've put m for metres in LaTeX for several of the answers but not all
I think you need to start the advice for each part with 'The area of a parallelogram is calculated using the formula...' instead of 'Paralellogram:'
you've put the word height in LaTeX in part c
in part d I would write 'half of a' instead of 'half a'
typo 'interpretted'
you have a space before a comma in part d
you've written 'this is shown below' but haven't shown below.

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Hannah Aldous 7 years, 9 months ago

Gave some feedback: Has some problems

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Aiden McCall commented 7 years, 9 months ago

Where it says shown below. I am hoping to insert GIFs of the explanation above. I am going to do this over the weekend; if it works i'll insert it if not I will omit the line and gap.

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Aiden McCall 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Aiden McCall 7 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Calculate the areas of polygons	Ready to use	Aiden McCall	20/11/2019 14:34
john's copy of Calculate the areas of polygons	draft	john halder	17/08/2017 14:36
Johan's copy of john's copy of Calculate the areas of polygons_oppervlakte vlakke figuren	draft	Johan Maertens	21/08/2017 20:27
Ryan's copy of Calculate the areas of polygons	draft	Ryan Poling	25/02/2019 22:25

There are 8 other versions that do you not have access to.

Question statement

Calculate the area of the following shapes.

Give any introductory information the student needs.

			Name	Type	Generated Value

h1	number	1.4
w1	number	5.7
wh11	number	7.980
wh11dp	number	8.0

			Name	Type	Generated Value

h2	number	2.5
w2	number	9.6
wh22	number	12.0000
wh22dp	number	12.0

			Name	Type	Generated Value

h5	number	2.4
w5a	number	6.2
w5b	number	9.5
wabh5dp	number	18.8
wabh5	number	18.84000

			Name	Type	Generated Value

w0	number	6.9
h0	number	2.2
wh00	number	15.180
wh00dp	number	15.2

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..4.5#0.1)

JME function reference

Description

The height of the parallelogram

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

Can an exam override the value of this variable?

Generated value: `number`

1.4

→ Used by:

wh11
wh11dp

"Part b)" → "Unnamed gap" - Minimum accepted value
"Part b)" → "Unnamed gap" - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
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Part b) Gap-fill
1. Gap Number entry
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Part c) Gap-fill
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Part d) Gap-fill
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Gap-fill

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

The area of the rectangle is Unnamed gap $\mathrm{m^2}$ . Round your answer to 1 decimal place.

Advice

The area of a rectangle is calculated using the formula

$\mathrm{Area} = \mathrm{base} \times \mathrm{height}\text{.}$

We have a base of $\var{w0}$ m and a height $\var{h0}$ m, therefore

$\begin{align} \mathrm{Area} &= \mathrm{base} \times \mathrm{height} \\ &= \var{w0} \times \var{h0} \\ &= \var{w0*h0} \\ &= \var{dpformat(w0*h0,1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \\ \end{align}$

$\begin{align} \mathrm{Area} &= \mathrm{base} \times \mathrm{height} \\ &= \var{w0} \times \var{h0} \\ &= \var{dpformat(w0*h0,1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \\ \end{align}$

The parallelogram is just a slanted rectangle:

Animation by Picknick.

Therefore, the area of a parallelogram is calculated using the formula

$\mathrm{Area} = \mathrm{base} \times \mathrm{height}.$

We have a base $\var{w1}$ m and perpendicular height $\var{h1}$ m.

$\begin{align} \mathrm{Area} &= \mathrm{base} \times \mathrm{height} \\ &= \var{w1} \times \var{h1} \\ &= \var{{w1}{h1}}\, \mathrm{m}^2 \\ &= \var{dpformat({w1}{h1},1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \\ \end{align}$

$\begin{align} \mathrm{Area} &= \mathrm{base} \times \mathrm{height} \\ &= \var{w1} \times \var{h1} \\ &= \var{dpformat({w1}{h1},1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \\ \end{align}$

c)

The area of a triangle is calculated using the formula

$\mathrm{Area} = \frac{\mathrm{base} \times \mathrm{height}}{2}.$

Note that the triangle is half of a rectangle:

Our triangle has a base $\var{w2}$ m and a height $\var{h2}$ m, therefore

$\begin{align} \mathrm{Area} &= \frac{1}{2} \times \mathrm{base} \times \mathrm{height} \\ &= \frac{1}{2} \times \var{w2} \times \var{h2} \\ &= \var{0.5*w2*h2}\, \mathrm{m}^2 \\ &= \var{dpformat(0.5*w2*h2, 1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \\ \end{align}$

$\begin{align} \mathrm{Area} &= \frac{1}{2} \times \mathrm{base} \times \mathrm{height} \\ &= \frac{1}{2} \times \var{w2} \times \var{h2} \\ &= \var{dpformat(0.5*w2*h2, 1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \\ \end{align}$

A trapezium can be interpreted as half of a parallelogram, this is shown below:

As we only want the area of one half of this shape, the area is half of

$\mathrm{area} = (a+b) \times \mathrm{height}\text{,}$

with ${a} = \var{w5a}$ m, ${b} = \var{w5b}$ m, and height $\var{h5}$ m.

$\begin{align} \mathrm{Area} &= \frac{(a+b)}{2} \times \mathrm{height} \\ &= \frac{(\var{w5a}+\var{w5b})}{2} \times \var{h5} \\ &= \var{(w5a+w5b)*0.5} \times \var{h5} \\ &= \var{(w5a+w5b)*(h5)/2}\, \mathrm{m}^2 \\ &= \var{dpformat((w5a+w5b)*(h5)/2, 1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \end{align}$

$\begin{align} \mathrm{Area} &= \frac{(a+b)}{2} \times \mathrm{height} \\ &= \frac{(\var{w5a}+\var{w5b})}{2} \times \var{h5} \\ &= \var{(w5a+w5b)*0.5} \times \var{h5} \\ &= \var{dpformat((w5a+w5b)*(h5)/2, 1)}\, \mathrm{m}^2 \quad \text{to 1 d.p.} \end{align}$

Give a worked solution to the whole question.

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Checkpoint description

Chris Graham 7 years, 7 months ago

Chris Graham commented 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Stanislav Duris commented 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Vicky Hall commented 7 years, 8 months ago

Aiden McCall 7 years, 9 months ago

Hannah Aldous commented 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Aiden McCall commented 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Error in variable testing condition

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Warning

Generated value: number

Parts

Gap-fill

Animation by Picknick.

c)

Generated value: `number`