﻿ Area: Measurement of a two dimensional figure or the surface of a 3-dimensional figure.

# Area

Pronunciation: /ˈɛəriə/ ?

 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Manipulative 1: Area of a rectangle. Created with GeoGebra.

An area is the measurement of an object in 2 dimensional space (2-space).[1] 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.

 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) 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. 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

Click on the 'Show Manipulatives' button below the table to see manipulatives for some of the figures.

FigureVariablesFormula
Area of 2-dimensional figures
Squares is length of a side.
Rectanglel is length of a side. w is the length of the second side.
Circler is the radius of the circle.
Triangleb is length of base. h is the length of the altitude of the base.
Regular Polygonn is the number of sides. s is the length of each side.
Surface area of 3-dimensional figures
Cubes is the length of one side.
Coner is the radius of the circle in the base. h is the height.
Cylinderr is the radius of the base. h is the height.
Table 1: Formulas for the areas of geometric figures.

• McAdams, David. Nets for Geometric Solids. LifeIsAStoryProblem.org. Life is a Story Problem.org. 2009-03-12. http://www.lifeisastoryproblem.org/explore/index_net.html.

### Educator Resources

Area. 2011-01-03. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/a/area.html.