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Mathematics

Perimeter, area and volume

Educator section

Memorandum

a)

(i) 9

(ii) 13

(iii) 16

b)

(i) 9 cm

(ii) 13 cm

(iii) 16 cm

  • area of square = length x 4

8.

a) 28 m; 45 m 2

b) 6 cm

c) 4 km; 24 km

d) 7 cm; 28 cm 2

e) 11 m; 11 m

9.2

a) 15 000; 1.5

b) 37 500; 3,75

c) 24 000; 2,4

9.3

a) 15 000 000; 15

b) 9 000 000; 9

c) 37 500 000; 37,5

Leaner section

Content

Activity: area [lo 4.2, lo 2.5, lo 2.3]

6. AREA

6.1 IMPORTANT to KNOW!

The area of a figure is the size of the flat surface that is included within the outside boundary of a figure. If you sweep your hand over this whole page, you have touched the whole surface of the page. If you paint a wall, we call the amount of space you have painted, the area.

6.2 Also IMPORTANT to REMEMBER:

Area is expressed in square units, e.g. square centimetre (cm2) or square metres (m2).

6.3 Memorise the following:

1 cm² = 10 mm x 10 mm = 100 mm²

1 m² = 100 cm x 100 cm = 10 000 cm²

1 km² = 1 000 m x 1 000 m = 1 000 000 m²

6.4 Ask your educator to photostat the following page or trace it just as it is:

a) Cut out the small squares and see how many of them will fit in the following figures.

(i)

__________________________________

(ii)

__________________________________

(iii)

__________________________________

b) What is the area of :

figure (i)? __________________________________

figure (ii)? _________________________________

figure (iii)? _________________________________

6.5.1 There is a quicker way to find out the area of figures!

We can use formulas,

e.g. rectangle

= length x breadth

= 5 x 2

= 10 cm2

6.5.2 Can you write down a formula that will determine the area of a square?

_____________________________________________________________________

7. Can you draw two different rectangles, each having an area of 48 cm²?

8. Work together with a friend and complete the following table:

Length Breadth Perimeter Area
E.g. 5 cm 3 cm 16 cm 15 cm 2
a) 9 m 5 m ________ ________
b) 6 cm ________ 24 cm 36 cm 2
c) 8 km ________ ________ 32 km 2
d) ________ 4 cm 22 cm ________
e) ________ ________ 44 m 121 m 2

9.1 Did you know?

The area of farms is calculated in hectares (ha).

1 ha = 100 m x 100 m

= 10 000 m²

9.2 Use your calculator and complete the following table:

Lengthm Breadthm Aream 2 Hectaresha
E.g. 100 100 10 000 1
a) 150 100 ___________ ___________
b) 250 150 ___________ ___________
c) 120 200 ___________ ___________

9.3 Complete the following with the help of your calculator:

Lengthm Breadthm Aream 2 Areakm 2
E.g. 2 000 500 1 000 000 1
a) 5 000 3 000 ___________ ___________
b) 1 500 600 ___________ ___________
c) 7 500 5 000 ___________ ___________

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;

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 2.3: We know this when the learner represents and uses relationships between variables in order to determine input and/or output values in a variety of ways.

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).

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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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