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Perimeter, area and volume

Educator section


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


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


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


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.


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.


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? ______________________


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

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
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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