An area is the measurement of an object in 2 dimensional space (2-space). For example, the area of a 2 meter by 3 meter rectangle is 2m · 3m = 6m2. Area can also refer to the measurement of the surface of an object in 3 dimensional space (3-space). The area of the surface of a cube with a side of 2 meters is 2m · 2m · 2m = (2m)3 = 8m3.
The surface area of a 3-dimensional geometric figure is the area of the boundary of the figure. If you take the boundary of a 3-dimensional 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 6s2 where s is the length of one side.
|Unit of Measure||Abbreviation||Equivalents|
|square meter||m2||1,000,000 m2 = 1 km2|
1 m2 ≈ 10.7639104 ft2
|square kilometer||km2||1,000,000 m2 = 1 km2|
1 km2 ≈ 0.386102159 mi2
|hectare||ha||1 ha = 10,000 m2|
1 ha ≈ 2.47 acres
|square foot||ft2||9 ft2 = 1 yd2|
1 ft2 ≈ 0.09290304 m2
|square yard||yd2||9 ft2 = 1 yd2|
1 yd2 ≈ 0.83612736 m2
|square mile||mi2||27,878,400 ft2 = 1 mi2|
1 mi2 ≈ 2.5899881 km2
|acre||--none--||1 acre = 43560 ft2|
600 acres = 1 mi2
1 acre ≈ 0.404685642 ha
|Table 1: Common units of measure of area|
Click on the 'Show Manipulatives' button below the table to see manipulatives for some of the figures.
|Area of 2-dimensional 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 3-dimensional 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.|
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