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The area of an ellipse is proportional to a rectangle having sides equal to its major and minor axes; The volume of a sphere is 4 times that of a cone having a base of the same radius and height equal to this radius; The volume of a cylinder having a height equal to its diameter is 3/2 that of a sphere having the same diameter;
The real area is 10,000 2 times the area of the shape on the map. Nevertheless, there is no relation between the area and the perimeter of an ordinary shape. For example, the perimeter of a rectangle of width 0.001 and length 1000 is slightly above 2000, while the perimeter of a rectangle of width 0.5 and length 2 is 5. Both areas are equal to 1.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
Given a rectangle with length l and width w, the formula for the area is: [2] 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: [1] [2] A = s 2 (square). The formula for the area of a ...
In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume, area, perimeter, etc. of the box. It is sufficient to find the smallest enclosing box for the convex hull of the objects in question. It is ...
In three-dimensional geometry, the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction. [1] [2] For instance, the girth of a unit cube in a direction parallel to one of the three coordinate axes is four: it projects to a unit square, which has four as its perimeter.
The area A of any triangle is the product of its inradius (the radius of its inscribed circle) and its semiperimeter: A = r s . {\displaystyle A=rs.} The area of a triangle can also be calculated from its semiperimeter and side lengths a, b, c using Heron's formula :
Roundness = Perimeter 2 / 4 π × Area . This ratio will be 1 for a circle and greater than 1 for non-circular shapes. Another definition is the inverse of that: Roundness = 4 π × Area / Perimeter 2 , which is 1 for a perfect circle and goes down as far as 0 for highly non-circular shapes.