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Mathematics

Perimeter, area and volume

Educator section

Memorandum

  • Bigger than a half + smaller than a half make 1 square, and the squares bigger than a half have been counted already

19.

a) 30

b) 40

c) 25

d) 35

e) 4 986

f) 2,51

g) 308

h) 71,2

i) 10

j) 40

k) 120

l) 1,743

m) 186

n) 1 528

o) 8,249

Leaner section

Content

Activity: area of irregular figures [lo 4.2, lo 2.5, lo 2.3]

16. AREA OF IRREGULAR FIGURES

16.1 a) Work together with a friend. How will you determine the area of this figure? Assume that every square is 1 cm2.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

b) Now use your method and determine the area!

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

16.2 Did you know?

With irregular figures, we can only determine an approximate area. We do it by counting all the whole squares within the figure. We also count all the squares that are bigger than half a square and add it to the first total. The squares that are smaller than half a square are not counted. Can you give a reason for this?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

This is how we express the approximate area in cm².

e.g.

Whole squares : 26

Squares bigger than half : 12

Approximate area :38 cm²

16.3 Now draw the outline of your hand on the squared paper below. Assume that each square is 1 cm².

a) Calculate the approximate area of your hand. __________________________

b) Which learner’s hand covered the biggest area? ________________________

c) Which learner’s hand covered the smallest area? ________________________

17 Time for self-assessment

  • Tick the applicable column:
Un­certain Reasonably certain Certain
I can explain the concept “area”.
I can convert cm² to mm² and vice versa.
I can convert m² tot cm² and vice versa.
I can convert km² to m² and vice versa.
I can convert m² to hectare and vice versa.
I know the formulas to determine the areas of the following figures:
  • square
  • rectangle
  • triangle
I can determine the area of regular figures.
I can determine the approximate areas of irregular figures.

18.1 Let us play a game!

You need a friend, two dice, paper and a pencil. Player A is the “perimeter” and player B is the “area”. You are both “rectangles” and work in cm.

Player A throws the two dice and then works out the perimeter of a rectangle with the two numbers, e.g. 6 and 2.

(6 x 2) + (2 x 2) = 16 cm

Player B calculates the area with the same numbers: 6 x 2 = 12 cm2

The perimeter is greater, thus player A gets two points. Take turns. The player who gets the most points after 15 rounds is the winner.

18.2 CHALLENGE!

a) Look carefully at this example of a house plan.

b) Now draw your own plan of a house as simply as possible.

c) What is the area of the floor surface of your house? _____________________

d) How big is your yard? ____________________________________________

e) What is the perimeter of your garage(s)? _____________________________

f) If you sell your house for half a million rand, what will the cost be per m²? _____________________________________________________________________

_____________________________________________________________________

g) If your parents build on another room 6,1 m by 3,5 m, what will the area of your house then be?

_____________________________________________________________________

_____________________________________________________________________

19. Let us now see if you can improve on the results of your previous mental test.

Complete the following as quickly and accurately as possible:

a) 0,6 of 50 = _______________________

b) 0,8 of 50 = _______________________

c) 50% of 50 = ______________________

d) 70% of 50 = ______________________

e) 4,986 x 1 000 = ___________________

f) 0,251 x 10 = ____________________

g) 3,08 x 100 = ______________________

h) 7,12 x 10 = ____________________

i) 25% x 40 = _______________________

j) 100% x 40 = ______________________

k) 300% x 40 = ______________________

l) 174,3 ÷ 100 = _____________________

m) 18,6 ÷ 0,1 = ______________________

n) 15,28 ÷ 0,01 = ____________________

o) 8 249 ÷ 1 000 = ___________________

Did you improve? ______________________

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 1.8: We know this when the learner performs mental calculations involving squares of natural numbers to at least 10 2 and cubes of natural numbers to at least 5 ³ .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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