© 2006  Rasmus ehf

Geometry - Area and surface

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Lesson 6

 

  Units of measurement for Area and Surface area

Units of measurement for Area:

km2 hm2 dam2 m2 dm2 cm2 mm2
      1 00 00  

 

1 m2 = 100 dm2  = 10000 cm2

 

A = 1m × 1m = 1m2
A = 10dm × 10dm = 100dm2
A = 100cm × 100cm = 10000cm2

 

    You know how to find the area of a plane, for example: 

     

 A = 3m × 2m = 6m2  six square metres.

If you are asked to give the answer in square centimetres, you can use the table below to help you convert the number. 

 

km2 hm2 dam2 m2 dm2 cm2 mm2
      6 00 00  

 

6m2 = 60000cm2

     Another method is to change metres to centimetres before finding the area. 

 

  = 

A= 300cm × 200cm = 60000cm2

 Surface area 

To find the surface area of a box you must find the area of each side or face of the box. 

3m × 4m = 12m2
2m × 3m = 6m2
2m × 4m = 8m2

12m2 + 6m2 + 8m2 = 26m2

Here you see the area of three of the sides. But the box has 6 sides.  Three more, the same as the ones above. The surface area of the box is therefore:  

26m2 × 2 = 52m2

To find the surface area of an object, you need to find out the shapes of the faces and calculate their areas.

Surface area of a pyramid =  area of a rectangle + the area of 4 triangles 
Surface area of a pyramid =   ++++

Surface area of a prism =    + + + +

 

Surface area of a can (cylinder) =    +   +

 

Area of the top
Area of the bottom Same as top

    If the label is flattened out, it is in the shape of a rectangle. 

A = length × width 

= 9cm × 25.12cm = 226.08cm2
This side is the circumference of a circle.
  

 

Surface area of a can (cylinder) =    +   +
A = 50.24cm2 + 50.24cm2 + 226.08cm2  = 326.56cm2

 

Surface area of a cone

Area of the top

Area of the bottom
Surface area of a sphere =

Practice these methods and then try Quiz 6 on Area. Remember to use the Checklist to keep track of your work.