
An area is the measurement of an object in 2 dimensional space (2space). For example, the area of a 2 meter by 3 meter rectangle is 2m · 3m = 6m^{2}. Area can also refer to the measurement of the surface of an object in 3 dimensional space (3space). The area of the surface of a cube with an edge of 2 meters is 2m · 2m · 6 sides = (2m)^{3} = 24m^{2}. 


The surface area of a 3dimensional geometric figure is the area of the boundary of the figure. The boundary of the figure is the surface between parts of the figure and the space which is not part of the figure. If you take the boundary of a 3dimensional object like a cardboard box, and bend it flat, you have a geometric net. You can use the net to calculate the surface area of the figure. Figure 2 shows a net of a cube. Since the surface of a cube consists of 6 squares, the total surface area is 6 times the area of a single square. So the surface area of a cube is 6s^{2} where s is the length of one side. 
Unit of Measure  Abbreviation  Equivalents 

square meter  m^{2}  1,000,000 m^{2} = 1 km^{2} 1 m^{2} ≈ 10.7639104 ft^{2} 
square kilometer  km^{2}  1,000,000 m^{2} = 1 km^{2} 1 km^{2} ≈ 0.386102159 mi^{2} 
hectare  ha  1 ha = 10,000 m^{2} 1 ha ≈ 2.47 acres 
square foot  ft^{2}  9 ft^{2} = 1 yd^{2} 1 ft^{2} ≈ 0.09290304 m^{2} 
square yard  yd^{2}  9 ft^{2} = 1 yd^{2} 1 yd^{2} ≈ 0.83612736 m^{2} 
square mile  mi2  27,878,400 ft^{2} = 1 mi^{2} 1 mi^{2} ≈ 2.5899881 km^{2} 
acre  none  1 acre = 43560 ft^{2} 600 acres = 1 mi^{2} 1 acre ≈ 0.404685642 ha 
Table 1: Common units of measure of area 
Manipulative  Figure  Variables  Formula 

Area of 2dimensional figures  
Square  s is length of a side. 

Rectangle  l is length of a side. w is the length of the second side.  
Circle  r is the radius of the circle.  
Triangle  b is length of base. h is the length of the altitude of the base.  
Regular Polygon  n is the number of sides. s is the length of each side.  
Surface area of 3dimensional figures  
Cube  s is the length of one side.  
Sphere  r is length of radius.  
Cone  r is the radius of the circle in the base. h is the height.  
Cylinder  r is the radius of the base. h is the height.  
Table 1: Formulas for the areas of geometric figures. 
#  A  B  C  D 
E  F  G  H  I 
J  K  L  M  N 
O  P  Q  R  S 
T  U  V  W  X 
Y  Z 
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