WISKUNDIGE GELETTERDHEID
GRAAD 10
NOG OEFENINGE
  
Omtrek en oppervlakte van 2D-figure.
  
MATHEMATICAL LITERACY
GRADE 10
MORE EXERCISES
  
Perimeter and area of 2D figures.
  
  
Vraag  / Question  1  
  
         Jy mag die volgende formules
         gebruik om onderstaande vrae
         te beantwoord :
         You may use the following formulae to
         answer to questions below :
  
  
         Gebruik die volgende afkortings :          Use the following abbreviations :
  
         Lengte / Length = l ;               Breedte / Breadth / Width = b 
         Hoogte / Height = h  ;             basis / base = b ;
         Middellyn / Diameter = d ;       straal / radius / radius = r 
         sy / side = s
         Omtrek / Perimeter = P ;
  
  
      Figuur                                          Omtrek (P)                        Oppervlakte ( A )
      Figure                                          Perimeter (P)                          Area ( A )
  
      Reghoek / Rectangle                      P = 2(l + b)                         A = lb
  
      Vierkant / Square                           P = 4 X s                            A = s2
  
      Driehoek / Triangle                         P = s1 + s2 + s3                 A = ½bh
  
      Sirkel / Circle                                 P = 2 X π X r                      A = π r2
  
      Sirkel / Circle                                 P = π X d                           A =  ¼ π d2
  
  
  
         Bereken die omtrek en oppervlakte van elke figuur :
         Calculate the perimeter and area of every figure :
  
  
                                       1.                                       2.                           3.
  

                                   [ A 1. ]                             [ A 2. ]                         [ A 3. ]
  
                                    4.                                     5.                                 6.
  

                                   [ A 4. ]                        [ A 5. ]                     [ A 6. ]
  
                                          7.                                                       8.
  

                                       [ A 7. ]                                          [ A 8. ]
  
                                              9.                                                              10.
  

                                           [ A 9. ]                                                      [ A 10. ]
  
  
         11.  Verwys na Figuur 9.  /  Refer to figure 9
         11.  Bereken die  /  Calculate the.
         11.1  omtrek van driehoek EBC  /  perimeter of triangle EBC         [ A 11.1 ]
  
         11.2  oppervlakte van  /  area of AECD                                         [ A 11.2 ]
  
  
   12.  Leerlinge moet help om die
          verspringput te bou :
          Hulle kry die volgende plan en
          gebruik dit om die berekeninge
          te doen :
  

          Die put het 'n vastrapplek van 1 m.
          Die res van die put is met sand
          gevul tot op 'n diepte van 300 mm.
   12.1  Bereken die oppervlakte van die put
            wat met sand gevul moet word.
                                                      [ A 12.1 ]
   12.2  Bereken die volume van
            die sand wat benodig word.
                                                      [ A 12.2 ]
   12.3  Bereken die koste van
            die sand as 1m3 sand R450 kos.
                                                      [ A 12.3 ]
  
   12.  Pupils have to assist to build
          the long jump pit.
          They obtain the following plan
          and use it to do the necessary
          calculations :
  

          The pit has a 1 m jumping platform.
          The rest of the pit is filled with sand
          to a depth of 300 mm.
   12.1  Calculate the area of the pit that
            has to filled with sand.
                                                               [ A 12.1 ]
   12.2  Calculate the volume of the sand
            required.
                                                               [ A 12.2 ]
   12.3  Calculate the cost of the sand if
            sand costs R450/m3
                                                              [ A 12.3 ]
  
Vraag  / Question  2  
  
  
  
         Jan wil die vloer van 'n kamer teël.
         Die diagram hierbo toon die
         afmetings van 'n teël en die kamer.
  
  2.1   Bereken die oppervlakte van die
          vloer. Jy mag die volgende
          formule gebruik :
            oppervlakte = lenge X breedte
                                                     [ A 2.1 ]
  2.2   Skakel die oppervlakte van die
          vloer om na mm2.
                                                     [ A 2.2 ]
  2.3   Bereken die aantal teëls wat
          nodig is. Jy mag die formule gebruik
                                     vloer oppervlakte
          Aantal teëls  =  ───────────
                                     teël oppervlakte
  
                                                     [ A 2.3 ]
  2.4   Bereken die aantal kartonne met
          teëls wat hy moet koop as
          1 karton 20 teëls bevat.
                                                     [ A 2.4 ]
  2.5   Bereken die koste vir die teëls as
          1 karton teëls R56,50 kos.
                                                     [ A 2.5 ]
         John wants to tile the floor of a room.
         The diagram above shows the dimensions
         of a tile and the floor.
  
  2.1   Calculate the area of the floor.
          You may use the following formula :
            area  =  length X breadth
  
                                                                [ A 2.1 ]
  2.2   Convert the area of the floor to
          mm2
                                                                [ A 2.2 ]
  2.3   Calculate the number of tile required.
          You may use the formula :
                                            area of floor
            Number of tiles  =  ─────────
                                             area of tile
  
                                                                [ A 2.3 ]
  2.4   Calculate the number of cartons
          containing the tiles that he has to
          buy if 1 carton contains 20 tiles.
                                                                [ A 2.4 ]
  2.5   Calculate the cost of the tiles if
          1 carton of tiles costs R56,50
                                                                [ A 2.5 ]
  
Vraag  / Question  3  
  
  

         Die diagram hierbo toon 'n
         klein dammetjie.
  
  3.1   Peter beweer dat die omtrek van
          die dam 25,7 m is. Is sy bewering
          korrek? Toon al jou berekeninge. :
                                                     [ A 3.1 ]
  3.2   Bereken die oppervlakte van
          die dam. Jy mag die formule
          oppervlakte = lengte X breedte gebruik.
                                                     [ A 3.2 ]
  3.3   Bereken die volume van die water,
          in m3 en i liter, wat nodig is om
          die dammetjie te vul as die dammetjie
          550 mm diep is.
          NB. volume = lengte X breedte X hoogte
          en 1 m3 = 1 000 ℓ
                                                     [ A 3.3 ]
  
         The diagram above shows a
         small pond.
  
  2.1   Peter claims that the perimeter of the
          pond is 25,7 m. Is his claim correct?
          Show all your calculations.
                                                               [ A 3.1 ]
  3.2   Calculate the area of the pond.
          You may use the formula :
          area = length X width
                                                               [ A 3.2 ]
  3.3   Calculate the volume of water,
          in m3 and in litres. necessary to fill the pond
          if the pond is 550 mm deep.
          N.B. volume = length X width X height and
          1 m3 = 1 000 ℓ
                                                               [ A 3.3 ]