Area

Area is the amount of space covered by a two-dimensional figure in a plane. It is the two-dimensional counterpart to length in one dimension, and volume in three dimensions.

Area in geometry

The area covered by a shape can be calculated from its 1-dimensional parameters, such as the length and width of a rectangle. The area of many geometric shapes can be determined by breaking shapes up into the simpler shapes that make them up. Refer to the geometry section for more detail.

Units of area

Area is commonly measured in terms of square units, where the "units" can be any number of units in the various systems of measurement. Square units are based on the measurement of area through the comparison of a given shape to squares of a fixed size. Take a look at the triangle in the square grid below as an example:

Each of the 9 small squares that make up the grid has an area of 1 square unit. Together, they make up an area of 9 square units. To find the area of the triangle, we can see that the triangle makes up half of the square and divide the square's area by 2 to find that the area of the triangle is 4.5 square units. We could also count the number of smaller squares that make up the triangle and see that there are 3 full squares, and 3 half squares, so 3 + (0.5) × 3 = 4.5 square units, the same result.

This is the basis for the measurement of area in terms of square units, where the area is measured by the number of squares with area of 1 square unit that make up the shape. We can replace "units" with the measurement of length in whatever system of measurement we want to use.

The most commonly used systems of measurement are the International System of Units (SI), US customary system, and imperial system of measurement. The following is a list of some of the commonly used units of area in these systems of measurement.

International System of Units:

Square meter (m²), square centimeter (cm²), square kilometer (km²).

US customary system and imperial system:

Square inch (in²), square foot (ft²), square mile (mi²), acre (ac).