Area

Pronunciation: /ˈɛəriə/ Explain

Click on the blue points and drag them to change the figure.

Calculate the area of the rectangle.
Manipulative 1 - Area of a Rectangle Created with GeoGebra.

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.

Click on the blue points and drag them to change the figure.

Calculate the area of the circle.
Manipulative 2 - Area of a Circle Created with GeoGebra.

Surface Area

Net of a cube
Figure 2: Net of a cube

The surface area of a 3-dimensional 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 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.

Common units measure of area

Unit of MeasureAbbreviationEquivalents
square meterm21,000,000 m2 = 1 km2
1 m2 ≈ 10.7639104 ft2
square kilometerkm21,000,000 m2 = 1 km2
1 km2 ≈ 0.386102159 mi2
hectareha1 ha = 10,000 m2
1 ha ≈ 2.47 acres
square footft29 ft2 = 1 yd2
1 ft2 ≈ 0.09290304 m2
square yardyd29 ft2 = 1 yd2
1 yd2 ≈ 0.83612736 m2
square milemi227,878,400 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

Areas of Common Geometric Figures

FigureVariablesFormula
Area of 2-dimensional figures
Squares is length of a side.
A=s^2
Rectanglel is length of a side. w is the length of the second side.
A=l*w
Circler is the radius of the circle.
A=pi*r^2
Triangleb is length of base. h is the length of the altitude of the base.
A=(1/2)b*h
Regular Polygonn is the number of sides. s is the length of each side.(1/4)*n*s^2*cot(pi/n)
Surface area of 3-dimensional figures
Cubes is the length of one side.A=6s^2
Spherer is length of radius.
A=4*pi*r^2
Coner is the radius of the circle in the base. h is the height.A=pi*r*square root(r^2+h^2)
Cylinderr is the radius of the base. h is the height.A=2*pi*r*h+2*pi*r^2
Table 1: Formulas for the areas of geometric figures.

More Information

  • McAdams, David E. Nets for Geometric Solids. lifeisastoryproblem.com. Life is a Story Problem LLC. 6/19/2018. http://www.lifeisastoryproblem.com/explore/index_net.html.

Educator Resources

Cite this article as:

McAdams, David E. Area. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/area.html.

Image Credits

Revision History

6/15/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (McAdams, David E.)
1/3/2011: Added common units of measure of area. (McAdams, David E.)
1/4/2010: Added "References". (McAdams, David E.)
12/19/2008: Changed equations to images. (McAdams, David E.)
10/27/2008: Changed manipulatives to GeoGebra. Added manipulatives to table of areas (McAdams, David E.)
6/7/2008: Corrected link errors. Corrected spelling (McAdams, David E.)
4/3/2008: Initial version. (McAdams, David E.)

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