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The area of a square is the product of the length of its sides. The perimeter of a square whose four sides have length is = and the area A is =. [1] Since four squared equals sixteen, a four by four square has an area equal to its perimeter.
That is, the area of the rectangle is the length multiplied by the width. As a special case, as l = w in the case of a square, the area of a square with side length s is given by the formula: [1] [2] A = s 2 (square). The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a ...
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
Consider completing the square for the equation + =. Since x 2 represents the area of a square with side of length x, and bx represents the area of a rectangle with sides b and x, the process of completing the square can be viewed as visual manipulation of rectangles.
Square miles should not be confused with miles square, a square region with each side having a length of the value given. For example, a region which is 20 miles square (20 miles × 20 miles) has an area of 400 sq mi; a rectangle of measuring 10 miles × 40 miles also has an area of 400 sq mi, but is not 20 miles square.
Comparison of 1 square foot with some Imperial and metric units of area. The square foot (pl. square feet; abbreviated sq ft, sf, or ft 2; also denoted by ' 2 and ⏍) is an imperial unit and U.S. customary unit (non-SI, non-metric) of area, used mainly in the United States, Canada, the United Kingdom, Bangladesh, India, Nepal, Pakistan, Ghana, Liberia, Malaysia, Myanmar, Singapore and Hong Kong.
The usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation n 2, usually pronounced as "n squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square (1 × 1). Hence, a square with side length n has area n 2.
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...