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Mathematics

Perimeter, area and volume

Educator section

Memorandum

10.

a) Yes, area of all three figures the same

b) area = (half of base) x height

11.1 1 867 km ²

11.2 530 m ²

11.3 9 m by 8 m

12.

13.1

a) 3 and a quarter square cm

b) 5 square cm

13.2 A

14.1

a) 64 cm ²

b) 180 cm ²

c) 81 m ²

d) 200 m ²

14.2

a) 42 m ²

b) 48 cm ²

c) 65 cm ²

d) 64 m ²

Leaner section

Content

Activity: area (brain-teaser) [lo 4.2, lo 1.9, lo 4.5]

10. BRAIN-TEASER!

A farmer divides his land as follows among his three children:

a) Was the farmer fair? __________________________ Motivate your answer:

_____________________________________________________________________

_____________________________________________________________________

b) From the above example, can you work out a formula that we use to determine the area of a triangle?

_____________________________________________________________________

11.1 Calculate the area of the farmer’s farm without the dam.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

11.2 What is the area of this lucerne camp on the farmer’s farm?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

11.3 The farmer wants to fence a rectangular camp with an area of 72m2. Problem: The perimeter must be kept to the minimum (because of the cost of the wire). What will the measurements of the camp be?

_____________________________________________________________________

12. A rectangular rugby field has a length of 110 m and a breadth of 60 m. What will it cost to plant grass which costs R6,45 per square metre?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

13.1 If each square is 1 cm2, what is the area of the shaded section?

a)

_____________________________________

b)

_____________________________________

13.2 Which figure has the biggest area: A or B?

A

_____________________________________

B

_____________________________________

14. BRAINTEASERS!

  • Work with a friend.

14.1 Can you determine the area of the shaded parts of each figure?

a)

_____________________________________

_____________________________________

_____________________________________

b)

_____________________________________

_____________________________________

_____________________________________

c)

_____________________________________

_____________________________________

_____________________________________

d)

_____________________________________

_____________________________________

_____________________________________

14.2 Calculate the areas of the following figures?

a)

_____________________________________

_____________________________________

_____________________________________

_____________________________________

b)

_____________________________________

_____________________________________

_____________________________________

_____________________________________

c)

_____________________________________

_____________________________________

_____________________________________

_____________________________________

d)

_____________________________________

_____________________________________

_____________________________________

_____________________________________

15. CLASS DISCUSSION

  • Let us discuss the following as a class:

15.1 Your school wants to build a new computer centre. The two possible plans that have been drawn up look like this:

A

B

  • Discuss:

a) Which plan would use the most bricks? Why?

b) Which plan would accommodate the most computers? Motivate.

c) Which plan will be the most expensive to build? Why?

15.2 A plan for a swimming pool for the school has also been drawn up:

a) What will happen to the area if the perimeter stays the same, BUT:

(i) the length increases and the breadth decreases?

(ii) the length decreases and the breadth increases?

b) When would the swimming pool have a maximum area?

Assessment

Learning Outcome 4: The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

Assessment Standard 4.2: We know this when the learner solves problems;

Assessment Standard 4.5: We know this when the learner calculates, by selecting and using appropriate formulae.

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.9: We know this when the learner uses a range of techniques to perform calculations.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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Maciej
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s. Reply
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Devang Reply
are you nano engineer ?
s.
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Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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Do you know which machine is used to that process?
s.
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SUYASH
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s. Reply
of graphene you mean?
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or in general
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in general
s.
Graphene has a hexagonal structure
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
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abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
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AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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Prasenjit
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Damian
not now but maybe in future only AgNP maybe any other nanomaterials
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I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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