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4.3 Area (brain-teaser)

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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

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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