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Sosiale wetenskappe


Graad 8


Module 14

Skaal en afstandsberekening

Skaal en afstandsberekening

1.1 Skaal

Skaal is die mate waarin ’n kaart kleiner is as die werklike aardoppervlakte. Julle het al vroeër geleer dat daar verskillende soorte skale is:

a) Die woordskaal druk die skaal in woorde uit, byvoorbeeld “Een sentimeter op die kaart verteenwoordig ’n halwe kilometer”.

b) Die breukskaal word as ’n verhouding of ’n breuk geskryf, byvoorbeeld 1:50 000 of 1 50 000 size 12{ { { size 8{1} } over { size 8{"50"`"000"} } } } {} .Dit beteken een eenheid (bv. cm) op die kaart verteenwoordig 50 000 van dieselfde eenhede (cm) op die aardoppervlakte.

c) Die lynskaal is ’n lyn wat in sentimeter afgemerk is, wat die ooreenkomstige afstand op die grond in kilometer aandui.

Afstandaangedui as 3,5 km

1.2 Die meet van afstand op ’n kaart

Daar gaan deurgaans van die topografiese kaartreeks gebruik gemaak word waar die skaal 1:50 000 is.

Gaan soos volg te werk om werklike afstand te bepaal:

  • Meet die afstand op die kaart akkuraat met ’n liniaal in sentimeter.
  • Herlei die afstand na km of m afhangend van wat gevra word.


  • Die kaartafstand tussen A en B is 10 cm.
  • Wat is die werklike afstand in km?
  • Wat is die werklike afstand in m?
10 cm × 50 000500 000 cm ÷ 100 000= 5 km 10 cm × 50 000500 000 cm ÷ 100= 5 000 m

Hoekom word daar met 100 000 en 100 gedeel?

  • Die metrieke eenheidsmate is soos volg:
  • Daar is dus 100 000 cm in ’n km 100 cm in ’n meter

Jy kan dus ’n korter metode gebruik as jy onthou dat jou skaal van 1:50 000 dieselfde is as:

1 cm = 50 000 cm1 cm = 500 m (÷ 100)1 cm = 0,5 km (÷ 100 000)

Bereken dan die afstand soos volg:

10 cm × 0,5 10 cm × 500= 5 km = 500 m

  • As ’n kronkelende pad byvoorbeeld gemeet moet word, moet die roete eers met ’n stukkie tou gemeet word. Meet die tou se lengte op die liniaal af en volg dan dieselfde metode as hierbo of meet dit af op die lynskaal.


[LU 1.3]

1. Bereken die werklike afstand in meter as die afstand op ’n 1:50 000 topografiese kaart die volgende is:

a) 2,3 cm

b) 6,8 cm

c) 5,5 cm

2. Bereken die werklike afstand in kilometer as die afstand op ’n 1:50 000 topografiese kaart die volgende is:

a) 90,4 cm

b) 56,3 cm

c) 103,6 cm


LU 1
Aardrykskundige OndersoekDie leerder is in staat om ondersoekvaardighede te gebruik om aardrykskundige en omgewingsbegrippe en -prosesse te ondersoek.
Dit is duidelik wanneer die leerder:
1.1 ‘n verskeidenheid geografiese en omgewingsbronne identifiseer en selekteer wat relevant tot die navorsing is;1.2 inligting vanaf kaarte en atlasse, asook grafiese en statistiese bronne, interpreteer;1.3 afstandberekening doen op kaarte en dit vergelyk met werklike afstand;1.4 fisiese en mensgemaakte eienskappe op lugfoto’s en kaarte identifiseer.



1(a) 1150 m

1( b) 3400 m

1(c) 2750 m

2(a) 45,2 km

2(b) 28,25 km

2(c) 51,8 km

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Source:  OpenStax, Aardrykskunde graad 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11035/1.1
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