Area

Pronunciation: /ˈæɹ.i.ə/ 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 an edge of 2 meters is 2m · 2m · 6 sides = (2m)³ = 24m².

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

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 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

Areas of Common Geometric Figures

Manipulative	Figure	Variables
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.

References

McAdams, David E.. All Math Words Dictionary, area. 2nd Classroom edition 20150108-4799968. pg 20. Life is a Story Problem LLC. January 8, 2015. Buy the book

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

Glide Ratio Activity (surface area). NASA LaRC Office of Education. 2/18/2010. http://www.archive.org/details/NasaConnect-Sof-GlideRatioActivity/index.htm.

Cite this article as:

McAdams, David E. Area. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/area.html.

Image Credits

All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/12/2019: Changed equations and expressions to new format. (McAdams, David E.)
1/20/2019: Corrected area of the surface of a cube. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
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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