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Area (oppervlakte) van poligone

  1. Area van driehoek: 1 2 × basis × loodregte hoogte
  2. Area van trapesium: 1 2 × (som van (parallelle) sye) × loodregte hoogte
  3. Area van parallelogram en rombus: basis × loodregte hoogte
  4. Area van reghoek: lengte × breedte
  5. Area van vierkant: sylengte × sylengte
  6. Area van sirkel: π x radius 2

Khan akademie video oor area en omtrek

Khan akademie video oor area van ʼn sirkel

Vind die area van die volgende figure:

  1. Ons moet eers vir BE, die loodregte hoogte van die parallelogram vind. Ons kan Pythagoras gebruik om dit te doen:
    BE 2 = AB 2 AE 2 BE 2 = 5 2 3 2 BE 2 = 16 BE = 4
  2. Ons pas die formule vir die area van ʼn parallelogram toe om die berekening te doen:
    Area = h × b = 4 × 7 = 28


  1. Sê of die bewering WAAR of VALS is in elk van die gevalle hieronder. Indien die bewering vals is, gee ʼn teen-voorbeeld om dit te staaf:
    1. Alle vierkante is reghoeke.
    2. Alle reghoeke is vierkante.
    3. Alle pentagone is gelykvormig.
    4. Alle gelyksydige driehoeke is gelykvormig.
    5. Alle pentagone is kongruent.
    6. Alle gelyksydige driehoeke is kongruent.
  2. Vind die areas vir elk van die gegewe figure. Onthou area word gemeet in vierkante eenhede (cm 2 , m 2 , mm 2 ).

Reghoekige prismas en silinders

In hierdie afdeling leer ons hoe om die oppervlakarea (buite-oppervlakte) en volume van reghoekige prismas en silinders te bereken. ʼn Reghoekige prisma is ʼn veelhoek wat uitgerek word in ʼn kolom sodat die hoogte van die kolom reghoekig tot sy basis is. ʼn Vierkantige prisma het ʼn vierkantige basis en ʼn driehoekige prisma het ʼn driehoekige basis.

Voorbeelde van ʼn vierkantige prisma, ʼn driehoekige prisma en ʼn silinder

Dit is eenvoudig om die oppervlakarea en volume van prismas te bereken.


Die term oppervlakarea verwys na die totale area van die oppervlak aan die buitekant van die prisma. Dit is makliker om te verstaan as ʼn mens aan die prisma dink as ʼn soliede voorwerp.

As jy die prismas in [link] bestudeer, sal jy sien dat die boonste syvlak van die prisma ʼn eenvoudige veelhoek is. Die driehoekige prisma het twee syvlakke wat driehoekig is en drie syvlakke wat reghoekig is. Om die oppervlakarea van ʼn prisma te bereken moet die oppervlak van elke syvlak bereken word en bymekaar getel word. ʼn Silinder bestaan uit twee sirkelvormige syvlakke en ʼn reghoekige kolom.

Oppervlakarea van Prismas

Bereken die area van elke syvlak en tel die areas bymekaar om die oppervlakarea van die prisma te bereken. Bepaal eers wat die regte vorm is van elke syvlak en bereken dan die area van daardie syvlak. Die oppervlakarea van die prisma is gelyk aan die som van die oppervlakareas van al die syvlakke.

Bespreking: oppervlakareas

In pare, bestudeer die volgende prismas saam met die diagram wat langs elke prisma vertoon word en verduidelik watter oppervlakareas elke prisma het. Verduidelik vir jou maat hoe elke diagram verband hou met die gepaardgaande prisma.

Aktiwiteit: oppervlakarea

Soek ʼn prentjie of neem ʼn foto van ʼn gebou wat nie ʼn eenvoudig gedefinieërde vorm het nie (byvoorbeeld een wat nie net ʼn reghoek is nie). Soek vir ʼn kasteel met torings of ʼn huis met gewels of ʼn stoep. Veronderstel jy moet die buitekant van die gebou verf. Hoeveel verf sal jy benodig? Dink aan dit wat jy geleer het omtrent oppervlakarea van poligone. Kan jy reëlmatige poligone in jou prent/foto vind en hulle gebruik om die oppervlakarea te bereken?

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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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