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# Calculating area oo a map

Module by: Siyavula Uploaders. E-mail the author

## CALCULATING AREA ON A MAP

Calculating area on a map.

Example

Steps:

1. Measure length in cm and convert to m / km.
2. Measure width in cm and convert to m / km.
3. Apply formula – L x W.
4. Write the answer in km² / m².

Always take note of the unit in which the answer must be given – this will usually be m² or km².

ACTIVITY 1: [LO 1.3]

1. The length of a rectangular object is 5,6 cm and the width is 3,4 cm on a 1 : 50 000 topographic map. Calculate the area of the object in km².
2. The length of a building is 1,1 cm and the width is 0,6 cm on a 1 : 50 000 topographic map. Calculate the area of the building in m².Calculating time between 2 points.

Remember the following:

The distance completed will have to be calculated from the map and be given in real km. Speed or time will always be provided.

How long will it take to travel by car at 60 km/h from point A to point B?

Steps:

ACTIVITY 2: [LO 1.3]

At what time will a person arrive at a destination if he or she leaves the house at 7:00 and travels a distance shown as 8 cm on a 1 : 50 000 map? Reading and analysing maps

Topographic maps are among the most useful and precise maps that are available because of the amount of detail that they contain and the precision with which the minutest details are indicated.

Topographic maps and orthophoto maps provide the geographer’s tools (SOURCE) and the reader needs to understand the language of the map. This makes it possible to give scientific explanations of features.

The activities that follow will help the learner to master map-reading techniques and skills and to extend his or her knowledge of Bloemfontein.

ACTIVITY 3: [LO 1.7]

• Find out where Bloemfontein is situated by using the index at the back of the atlas.
• In which province of South Africa is Bloemfontein?
• Indicate the direction to Durban from Bloemfontein.
• Measure the distance between Edenburg (south of Bloemfontein) and Bloemfontein in km, using the linear scale given for the map in your atlas.
• At what time will a bus arrive in Bloemfontein if it leaves Edenburg at 10:00 and travels at an average speed of 120 km/h, without stopping along the way?
• Read the accompanying text and answer the questions dealing with Bloemfontein’s past.

Provide reasons for the city’s:

1. origin;
2. development as a city.
• The development of Bloemfontein
• More that a hundred years ago, trekkers from the Cape settled in the environment of Bloemfontein, which quickly developed into a centre for trading. In 1846, the location of the present city was selected by Major Warden as the most convenient site for building a fort and a residential area. From this beginning, and in spite of setbacks resulting from unrest and wars, which inhibited its development, the small town developed into an attractive city.
• Bloemfontein forms the geographical hub of South Africa’s railway, road and airline services. The development of the Free State gold mines, less than 160 km from the city, has brought additional prosperity to the city, which is fast becoming an important industrial centre.
• The city is situated in a picturesque environment in the heart of the Free State plateau, surrounded by hillocks and hills rising high above the plains. To the north is Naval Hill, from where there is a particularly beautiful view of the city.

ACTIVITY 4: [LO 1.3]

Study the accompanying extract from the 1 : 50 000 topographic map of South Africa, sheet 2926 AA Bloemfontein, and orthophoto 2926 AA 9 Spitskop and answer the following questions:

1. Identify the features of the landscape that occur at the following coordinates:

a) 29º05'40" S, 26º09'20" E.

b) 29º06' S, 26º10'35" E.

2. Indicate the position of the 2926 AA Bloemfontein map sheet by means of a simple sketch:

Indicate which map sheet lies directly to the:

a) North

b) West

c) South ______ of 2926 AA.

1. Indicate the position of the 2926 AA 9 Spitskop orthophoto by means of a simple sketch:
1. 1 (a) How does the scale of a topographic map and of an orthophoto differ?

Which scale is larger?

• What can you identify with regard to recreation facilities available to the inhabitants of Bloemfontein by careful investigation of the topographic map and the orthophoto?
• Why do we observe a considerable number of wind pumps in the environment?
• Study the precipitation figures for Bloemfontein that are provided below:
 J F M A M J J A S O N D Rainfall in mm 91,4 78,7 76,2 55,9 25,4 7,6 10,2 11,2 15,5 50,8 66 62,3
1. (a) Draw a column graph to represent the rainfall data. Use a vertical scale of 1 cm to 10 mm.
1. (b)1. Which season has the highest rainfall?
1. (c)1. Which month receives the highest rainfall?

ACTIVITY 5: [LO 1.4]

1. A cellular telephone service provider wants to erect a communications tower for the cellular phone service. It has to be situated on the highest point in the area. Provide the height in metres of the highest point indicated on the map. Also provide the coordinates for the specific point.

2. Provide a reason why the observatory (Observatory Theatre) was built on Naval Hill (29°05’45” S, 26°14’20” E) and not in a more central part of the city.

3. Calculate magnetic north from trigonometry beacon Δ 50 (29°03’45” S, 26°10’50” E). Show all calculations.

4. How long will it take a traveller to go from the one N1 intersection (29°07’45” S, 26°10’ E) to the other N1 intersection (29°05’30” S, 26°10’20” E) if an average speed of 120 km/h is maintained?

5. Calculate the area of the terminal building of the railway line (square black building) at 29°06’50” S, 26°14’50” E. Show all calculations.

6. What is true north from Δ 174 (29°05’25” S, 26°11’30” E) to the peak of Spitskop (29°05’40” S, 26°9’20” E.)

ACTIVITY 6: [LO 1.2]

Use the orthophoto only and answer the following questions:

1. Is this orthophoto a vertical or an oblique aerial photograph?
2. Which part of Bloemfontein is shown on the orthophoto? Indicate the exact position with faint pencil lines on the 1 : 50 000 or topograpic map sheet.
3. What is the real distance in km from the N1 road junction near Tempe (at Dam van Trane) to the road junction near Rayton in the northeast?
4. In which direction do you travel from the Tempe road junction to the road junction near Rayton?
5. Which kind of activity will take place at Tempe? Look at the long buildings arranged in rows that are there, in particular. What is the direction in which the shadows of these buildings fall?
1. (b)1. At what time of day, therefore, was the photograph taken?

ACTIVITY 7: [LO 2.2]

Make a poster about Bloemfontein. It must be eye-catching to attract visitors and tourists.

Your poster should present the following information:

1. (a)1. Tourist attractions.
1. (b)1. The recreational facilities of the city.
1. (c)1. Extra-mural activities offered by the city.

## Assessment

 Learning Outcomes(LOs) LO 1 Geographical EnquiryThe learner will be able to use enquiry skills to investigate geographical and environmental concepts and processes. Assessment Standards(ASs) We know this when the learner: 1.2 asks questions that are relevant for identifying sources; 1.3 draws conclusions and makes analyses to obtain information from sources such as photographs, maps, atlases, graphs and statistics; 1.4 correlates information from different sources; 1.7 reports on knowledge that they have obtained through research, making use of different sources of information. LO 2 Geographical Knowledge and UnderstandingThe learner will be able to demonstrate geographical and environmental knowledge and understanding. We know this when the learner: 2.2 identifies ways in which Science and Technology have contributed a positively and negatively influence to development (people and resources.)

## Memorandum

ACTIVITY1:

1. L × B

(5,6 × 0,5) × (3,4 × 0,5)

2,8 × 1,7

= 4,76 km2

• L × B

(1,1 × 500) × (0,6 × 500)

550 × 300

165 000 m2

ACTIVITY 2:

DistanceSpeed1. Actual distance = 8 × 0,5 = 4 km

Time =

= 4km80km/h4km80km/h size 12{ { {4 ital "km"} over {"80" ital "km"/h} } } {}

= 0,05 × 60

= 3 minutes

• 7:00 + 3 minutes

= 7:03

ACTIVITY 3:

1. 29008’ S, 26015’E
2. Free State
3. ESE
4. ± 70 km
5. Time = DistanceSpeedDistanceSpeed size 12{ { { bold "Distance"} over { bold "Speed"} } } {}

= 70km120km/h70km120km/h size 12{ { {"70" ital "km"} over {"120" ital "km"/h} } } {}

= 0,583 × 60

= 34,98 minutes

• 10:00 + 34,88 = 10:34,98
• Origin of Bloemfontein
1. a) People who migrated from the Cape settled there.
2. b) In 1846 Major Warden chose it as a suitable place to build a fort and settlement.

Development of Bloemfontein

• Initially it quickly developed into a trading centre.
• Wars and insurrection did not halt the growth.
• Geographic centre of rail, road and air transport.
• Gold-fields 160 km away boost growth.
• Today an important industrial centre.
• Tourism is flourishing thanks to picturesque surroundings.

ACTIVITY 4:

1a) Pointed hill

b) Flat-topped hill (Naval Hill)

3a) 2826 CC

b) 2925 BB

c) 2926 AC

4.

5a) Topographical map = 1:50 000

Orthophoto = 1:10 000

b) Topographical 1:50 000 is a smaller scale

• Motor or motorcycle racing, camping in caravan park, golfing, hang-gliding, flying aeroplanes, visiting zoo, visiting parks, visiting botanical gardens, playing sports on sports fields, swimming in rivers and dams, sailing on dams, visiting observatory, etc.
• Windmills are used to retrieve underground water for consumption. Therefore it must be relatively dry here with intermittent rainfall.

8 (a)

1. a) Winter
2. b) January

ACTIVITY 5:

1. Highest point 1499

Co-ordinates: 290 05’ 50” S 260 13’ 20’ E

1. Higher, flat area from where there is a good view.

City lights and pollution have smaller effect here.

3. True North / Bearing : 1640

Magnetic Declination : 2001 – 2003 = 2 years

2 × 6’ westwards (+)

20035’ + 12’

= 20035’ west of true north

Magnetic Bearing = 640 + 20035’

= 184035’

4. Map distance = 8,5 cm × 0,5 = 4,25 km

Time = DistanceSpeedDistanceSpeed size 12{ { { bold "Distance"} over { bold "Speed"} } } {}

= 4,25km120km/h4,25km120km/h size 12{ { {4,"25" ital "km"} over {"120" ital "km"/h} } } {}

= 0,35 × 60

= 2,1 minutes

1. L × B

(0,9 × 500) × (0,5 × 500)

450 × 250

= 112 500m2

6. Actual bearing = 2660

ACTIVITY 6:

1. Vertical
2. Learners do on map
3. Actual distance = 26,6 cm on a 1:10 000 map

26,6 × 0,1

= 2,66 km

1. North-east
2. Defence Force training centre

Many soldiers who live in barracks

6.a) South-east

b) Afternoons

ACTIVITY 7:

In order for a poster to catch the eye, it must be easy to read.

Make use of photos, sketches, etc. and limit the text to a minimum by listing only the most important facts.

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