Area
Read this article to learn more about what area is, how to find area, and how to express the results once you have found the area. Get some basic formulas for finding area of triangles, circles, rectangles, squares, and parallelograms.
In the real estate market, in interior decorating, in planning a garden, any time a reference is made to square feet, square yards, square meters, square miles, square kilometers, acres (4840 square yards), and hectares (a unit equal to 10,000 square meters) what’s being discussed is area. To understand more about area, continue reading this article.
What Is Area?
Area is the size of a two-dimensional plane with a closed boundary. Surface area, on the other hand, is the sum of the area of the outside surfaces of a three-dimensional solid. In either case, it is expressed in square units, which in the United States may be U.S. Customary Units, or standard units, such as feet, yards, and miles or units from the International System of Units, also known as the metric system or SI, which includes meters and kilometers.
The Units of Area and Their Names
Let’s begin by looking at the units of area. Area is found by multiplying one distance by another distance, both expressed in exactly the same units. Distance is expressed by units like feet, yards, meters, miles, and kilometers. The results are expressed in square units, which can be written with the word square, the abbreviation sq., or the superscript 2 following the unit, and the unit may be abbreviated as well, like this:
square feet | sq. feet | sq. ft. | feet^{2 }or ft.^{2} |
square meters | sq. meters | sq. m | meters^{2 }or m^{2} |
square yards | sq. yards | sq. yd. | yards^{2 }or yd.^{2} |
square miles | sq. miles | sq. mi. | miles^{2 }or mi.^{2} |
square kilometers | sq. kilometers | sq km | kilometers^{2 }or km^{2} |
Note that in the SI system, not only are the same abbreviations used for singular and plural forms of the same unit, but no periods are used. On the other hand, with standard units, periods are used in some style systems, although it is similar to SI in using the same abbreviations for singular and plural units. The units called acres and hectares are only used to express the results, not to find the area and they are units of area, so do not have the indication square at any time or in any form.
The Units of Area and How They Relate
Here
Unit | Conversion | New Unit |
ft.^{2} | 0.09290304 | m^{2} |
m^{2} | 10.7639104 | ft.^{2} |
yd.^{2} | 0.83612736 | m^{2} |
m^{2} | 1.19599005 | yd.^{2} |
mi.^{2} | 2.58998811 | km^{2} |
km^{2} | 0.386102159 | mi.^{2} |
Note that for many purposes, it might be appropriate to round these numbers. To read more about rounding, see the article “Rounding Numbers.”
Formulas for Area
The standard formulas for area can be quite useful. Here are the formulas for basic geometric shapes (for more on shapes, see the article “Geometric Shapes”).
A triangle is a polygon with three sides. The formula for the area of a triangle is:
A = ½ bh
where A is the area, b is the length of the base, and h is the height of the figure. In a triangle that is not equilateral (that is, when the sides are not all the same length), one may choose any side to be the base.
A parallelogram is a polygon with four sides (a quadrilateral) and two sets of parallel sides. The formula for the area of a parallelogram is:
A = bh
where A is the area, b is the length of the base, and h is the height of the figure. You might want to take a moment to compare this to the formula for a triangle, so you see the relationship and don’t confuse them.
A rectangle is a quadrilateral with four right angles. Since the base of a rectangle is the length of one set of sides and the height is the length of the other set of sides, the area of a rectangle can be expressed like this:
A = ab
where A is the area, a is the length of one side, and b is the length of the other side.
For squares, which are rectangles with equal and parallel sides, the formula can be simplified to this:
A = s^{2}
where A is the area and s is the length of one side.
A circle is a geometric figure with a boundary formed of points that are equidistant from its center. The length from the center to any point on the perimeter is called the radius (for more about perimeter, see the article of that name). The formula for the area of a circle is
A = πr^{2}
where A is the area, π is the constant pi (3.14159), and r^{2} is the radius squared.