john's copy of Calculate the areas of polygons

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john halder

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john halder 7 years, 7 months ago

Created this as a copy of Calculate the areas of polygons.

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

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Question statement

Calculate the area of the following shapes.

Give any introductory information the student needs.

			Name	Type	Generated Value

h1	number	4.5
w1	number	5.2
wh11	number	23.400
wh11dp	number	23.4

			Name	Type	Generated Value

h2	number	3.5
w2	number	8.8
wh22	number	15.4000
wh22dp	number	15.4

			Name	Type	Generated Value

h5	number	2.5
w5a	number	5.3
w5b	number	7.5
wabh5dp	number	16.0
wabh5	number	16.00000

			Name	Type	Generated Value

w0	number	8.1
h0	number	2.3
wh00	number	18.630
wh00dp	number	18.6

			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`

4.5

→ 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
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Number entry
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1. Step Information only
Part c) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part d) Gap-fill
1. Gap Number entry
  Add
1. Step Information only

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.

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

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

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john's copy of Calculate the areas of polygons

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Taxonomy: mathcentre

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Checkpoint description

john halder 7 years, 7 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

Animation by Picknick.

c)

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john's copy of Calculate the areas of polygons

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

john halder 7 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Animation by Picknick.

c)

Generated value: `number`