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Mathematics

Perimeter, area and volume

Educator section

Memorandum

3.2

250 mm

320 mm

3.3

a) 135 mm

b) 135 mm

c) 104 mm

d) 174 mm

3.4

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)

3.5

By means of a piece of string or wool

3.6

a) 3 100 km

b) 500 km

c) 350 km

d) 15,45 h

38.

a) 42

b) own answer

c) R2,681,70

5.

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

Content

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

3. PERIMETER

3.1 IMPORTANT to REMEMBER!

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?

Pentagon:

Octagon:

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

a)

______________________________________

b)

_____________________________________

c)

_____________________________________

d)

_____________________________________

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?

a)

b)

______________________________________________________________

______________________________________________________________

______________________________________________________________

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:
I did WELL REASONABLY NOT SO WELL

Assessment

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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
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
good afternoon madam
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
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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