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Perimeter, area and volume

Educator section



250 mm

320 mm


a) 135 mm

b) 135 mm

c) 104 mm

d) 174 mm


a) area = 2 x (b + d) or area = (2 x b) + (2 x d)

b) area= 2 x (f+g) or area = (2 x f) + (2 x g)

c) area = 4 x k

d) area = (2 x a) + (2 x e) or area = 2 x (a + e)


By means of a piece of string or wool


a) 3 100 km

b) 500 km

c) 350 km

d) 15,45 h


a) 42

b) own answer

c) R2,681,70


a) 27

b) 27

c) 39

d) 18

e) 18

f) 9

g) 14

h) 2

i) 12

j) 60

k) 60

l) 64

m) 72

n) 125

o) 108

Leaner section


Activity: perimeter [lo 2.5, lo 4.2, lo 4.3, lo 1.8]



The perimeter of any figure is the total length around a figure, in other words the sum of the lengths of all the sides.

Perimeter is thus a length and is measured in millimetres, metres or kilometres. The most accurate method to determine perimeter is to use compasses and a ruler.

3.2 What is the perimeter of your pentagon and octagon above?



3.3 Use your ruler and determine the perimeter of the following polygons:









3.4 Work together with a friend. Work out formulas to determine the perimeters of the following quadrilaterals:

a) A rectangle with a length of b centimetres and breadth of d centimetres:




b) A parallelogram with sides f centimetres and g centimetres:




c) A rhombus with sides k millimetres:




d) A kite with sides a millimetres and e millimetres:




3.5 How will you determine the perimeter of the following figures?






3.6 A grade 7 class leaves on a tour.

a) Look at the accompanying sketch and use the scale to find out how far they will travel.

1 : 100

1 cm = 100km

b) What is the actual distance from E to B? _____________________________

c) What is the actual distance from B to D? _____________________________

c) If the bus travels at 110 km/h, how long will it take for the bus to travel from A to F if it doesn’t stop along the way?


3.8 The sketch shows a camp for sheep that needs to be fenced.

a) If the horizontal poles are 2,7 m long, and you leave an opening of 1,5 m for a gate, how many upright poles are you going to need?



b) Where are you going to leave an opening for a gate? Motivate your answer.



c) If the upright poles cost R63,85 each, how much will the farmer have to spend?



4. Time for self-assessment

  • Tick the applicable block:
Yes No
I could find solutions to the brainteasers.
I was able to draw a regular pentagon.
I was able to draw a regular octagon.
I can explain the concept “perimeter”.
I could calculate accurately the perimeter of the polygons.
I was able to formulate and write down the formulas for perimeter of the following:
  • rectangle
  • parallelogram
  • rhombus
  • kite
I was able to calculate accurately, according to scale, the distance that the Grade 7’s would have covered on their tour.
I was able to correctly calculate the number of poles that the farmer needed for his camp.

5. Let us test your mental maths now!

Complete the following as quickly and accurately as possible:

a) 6 + 7 x 3 = ............

b) 6 + (7 x 3) = ............

c) (6 + 7) x 3 = ............

d) 9 x 6 ÷ 3 = ............

e) 9 x (6 ÷ 3) = ............

f) 36 ÷ (12 ÷ 3) = ............

g) 13 – 5 + 6 = ............

h) 13 – (5 + 6) = ............

i) 14 – (5 – 3) = ............

j) 4 x 3 x 5 = ............

k) 5 x (3 x 4) = ............

l) 43 = ............

m) 32 x 23 = ............

n) 53 = ............

o) 33 x 22 = ............

  • Complete by colouring:


Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.5: We know this when the learner solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x - 8 = 4).

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 4.3: We know this when the learner solves problems using a range of strategies;

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

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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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
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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