4.3 Area (brain-teaser)

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:

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b) From the above example, can you work out a formula that we use to determine the area of a triangle?

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11.1 Calculate the area of the farmer’s farm without the dam.

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11.2 What is the area of this lucerne camp on the farmer’s farm?

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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?

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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?

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13.1 If each square is 1 cm2, what is the area of the shaded section?

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b)

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13.2 Which figure has the biggest area: A or B?

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14. BRAINTEASERS!

• Work with a friend.

14.1 Can you determine the area of the shaded parts of each figure?

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c)

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d)

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14.2 Calculate the areas of the following figures?

a)

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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

• 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.