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Oppervlakte van vorms.

2cm. 12m. A1. A2. 7cm. 10m. 5cm. A1. 3cm. 12cm. A2. 16m. 8cm. Oppervlakte van vorms. 1cm 2. 1cm. 1cm. 1cm 2. Wat Is oppervlakte ?. Oppervlakte is die hoeveelheid spasie :. Area. Area. Area. Area. Area. Area. Area. Area. Area. Area. Area. Area. Area. Area. Area.

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Oppervlakte van vorms.

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  1. 2cm 12m A1 A2 7cm 10m 5cm A1 3cm 12cm A2 16m 8cm Oppervlakte van vorms.

  2. 1cm2 1cm 1cm 1cm2 Wat Is oppervlakte ? Oppervlakte is die hoeveelheid spasie : Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Oppervlakte word gemeet in cm2. ‘n Vierkante cm is ‘n vierkant met 1 sentimeter in elke rigting Dit word so geskryf:

  3. B A C D Skat die oppervlakte. Rangskik in volgorde van grootste oppervlakte tot kleinste oppervlakte

  4. B A C D Elke vorm bestaan uit 36 blokkies van 1cm2

  5. Breedte lengte C Oppervlakte van ‘n reghoek. Opp = L x B of bh

  6. (1) (2) (3) (4) Opp= L x B A = 12 x 3 =36cm2 Opp. = L x B Opp. = 6 x 6 =36cm2 Opp.= L x B Opp.= L x B Opp. = 9 x 4 =36cm2 Opp. = 18 x 2 =36cm2

  7. 2cm 5cm A1 A1 3cm A2 A2 8cm Oplossing 2 3 5 6 Opp. = A1 + A2 Opp = ( 2 x 5) + (6 x 3) = 10 + 18 Opp = 28cm2

  8. (1) (2) 6cm 2.7m 8cm 4.2m 17cm (3) 5cm 12cm 8cm Wat kom in die boks ? Vind die oppervlaktes: 48cm2 11.34m2 141cm2

  9. 12m 10m A1 A1 16m A2 A2 Voorbeeld Oplossing. Verdeel die figuur in twee: Opp = A1 + A2 10 10 12 16-12 =4 Opp = LB + 1/2 BH = 10 x 12 + ½ x 4 x 10 = 120 + 20 = 140m2

  10. (1) (2) 6.3m 10cm 10.2 m 8cm 18m (3) 12m 25m Wat kom in die boks? 2 Bereken die oppervlaktes: 40cm2 32.13m2 258m2

  11. Die oppervlakte van ‘n trapesium. ‘n Trapesium het slegs 1 paar teenoorstaande sye wat ewewydig is

  12. b h a A1 A1 A2 A2 A3 A3 Opp = A1 + ( A2 + A3 ) Opp = b x h + ½ x (a - b) x h Opp = bh + ½ h(a - b) Deel die trapesium in drie dele: Opp = bh + ½ ah – ½ bh Opp = ½ ah + ½ bh Opp. = ½ h ( a + b ) b h Jy kan dikwels net “common sense” gebruik as jy die formule vergeet het h a – b

  13. 11cm 13cm 16cm Voorbeeld 1 Bereken die oppervlakte van die trapesium: Oplossing: gebruik formule Opp = ½ h ( a + b ) a = 16 b =11 h = 13 Opp. = ½ x 13 x ( 16 + 11 ) Opp. = ½ x 13 x 27 Opp. = 175.5cm2

  14. 11cm 13cm 16cm Oplossing ( Saamgestelde figure). Verdeel die trapesiun in dele: Opp = reghoek + driehoek Opp = LB + ½ BH Opp = (11x 13) + ( ½ x 5 x 13 ) Opp = 143 + 32.5 Opp = 175.5cm2 11 Besluit self of jy die formule wil gebruik of saamgestelde figure 13 13 16 – 11 = 5

  15. 8m 14m 10m Voorbeeld 2 Verdeel die figuur in dele: Opp = reghoek + driehoek Opp = LB + ½ B H opp = ( 10 x 8 ) + ( ½ x 6 x 10 ) Opp = 80 + 30 Opp = 110 m 2 10 10 14 – 8 = 6 8

  16. 13cm (1) 10cm (2) 20cm 5.4m 4.9m 2.7m Wat gaan in die boks? 3 Bereken die oppervlaktes: 165cm2 19.85m2 (tot 2 d.p)

  17. Die oppervlakte van ‘n ruit. ‘n Ruit is ‘n soort parallellogram behalwe dat al die sye ewe lank is. Die hoeklyne halveer mekaar ook reghoekig h b Opp. = basis x loodregte hoogte = bh

  18. Die oppervlakte van ‘n ruit. A B Stel AC = m en BD = k In driehoek ADC Opp = ½ bh =½ m ½ k = In driehoek ABC Opp = ½ bh = ½ m ½ k = C D + mk mk Opp. = mk = AC x BD

  19. 5cm Height 8 cm Base The Area Of A Triangle. Consider the right angled triangle below: What is the area of the triangle ? Area = ½ x 40 = 20cm2 What shape is the triangle half of ? The formula for the area of a triangle is: Rectangle Area = ½ x Base x Height What is the area of the rectangle? A = ½ BH Area = 8 x 5 = 40 cm2

  20. Height (H) Base (B) A1 A2 H A1 A2 B Does the formula apply to all triangles ? Can we make this triangle into a rectangle ? Yes The triangle is half the area of this rectangle: The areas marked A1 are equal. The areas marked A2 are equal. For all triangles: Area = ½ BH

  21. 6cm 3.2m 10cm 6.4m Calculate the areas of the triangles below: Example 1 Example 2 Solution. Solution. Area = ½ x base x height Area = ½ x base x height height = 6cm base = 10 cm height = 3.2m base = 6.4m Area = ½ x 10 x 6 Area = ½ x 6.4 x 3.2 Area = ½ x 60 = 30cm2 Area = ½ x 20.48 = 10.24m2

  22. Die oppervlakte van ‘n sirkel. Deel ‘n sirkel in vier ewe groot dele: Maak ‘n vorm soos hieronder Ons kan amper ‘n reghoek vorm WAT DAARVAN?

  23. L B Verdeel nou dieselfde sirkel in 8 ewe groot dele Die agt dele word in dieselfde patroon verdeel Nou kan jy die reghoek beter sien:

  24. B L Die lengte van die reghoek - watter deel van die sirkel is dit? En die breedte? Helfte van die omtrek van die sirkel x radius. As die omtrek = 2  r dan is die L van die sirkel dus =  r .

  25.  r . r Gevolgtrekkeing r Die oppervlakte van ‘n sirkel =  r 2. Die oppervlakte van die reghoek (sirkel)? Opp =  r x r Opp =  r 2 See “Autograph Extras”, “New”, “Area Of Circle” for further info’.

  26. 2.7m 20 cm Bereken die oppervlaktes van die sirkels: Voorbeeld 2 Voorbeeld 1. Opp =  r 2 Opp =  r 2 r = 1.35m r = 10 = 3.14 x 1.35 x 1.35 = 3.14 x 10 x 10 = 5.72m2( to 2 d.p) = 314 cm2

  27. A1 A2 7cm 7cm 12cm Opp. =  r 2 2 Opp. = 3.14 x 7 x 7 2 Voorbeeld 4 Voorbeeld 3 Verdeel die figuur in twee dele. Bereken die helfe die opp. V van ‘n sirkel: Opp. = A1 + A2 = LB + ½  r 2. L = 12 B = 7 r = 3.5 Opp. = 12 x 7 + ½ x 3.14 x 3.5 x 3.5 Opp. = 84 + 19.23 Opp. = 76.93cm2 Opp. = 103.2cm 2. (to 1 d.p)

  28. (1) (2) 6.3m 7cm (3) 4.2cm 6.7cm Wat is in die boks ? 4 Bereken die oppervlakte van die volgende: 153.86cm2 31.16m2 ( 2 d.p) 35.1cm 2 ( 1 d.p)

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