Area
Area
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).
Video: Learning about Area
Area formulas
Polygon formulas
Video: Perimeter and area of a non-standard polygon | Perimeter, area, and volume
For a non-self-intersecting (simple) polygon, the Cartesian coordinates (i=0, 1, ..., n-1) of whose n vertices are known, the area is given by the surveyor's formula:
(i=0, 1, ..., n-1) of whose n vertices are known, the area is given by the surveyor's formula:
where when i=n-1, then i+1 is expressed as modulus n and so refers to 0.
Rectangles
The area of this rectangle is lw.
The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length l and width w, the formula for the area is:
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A = lw (rectangle).
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:
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A = s2 (square).
Video: Area of a Rectangle
The formula for the area of a rectangle follows directly from the ........
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