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In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
The area of the parallelogram is the area of the blue region, which is the interior of the parallelogram. The base × height area formula can also be derived using the figure to the right. The area K of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles. The area of the ...
A convex quadrilateral is orthodiagonal if and only if its Varignon parallelogram (whose vertices are the midpoints of its sides) is a rectangle. [6] A related characterization states that a convex quadrilateral is orthodiagonal if and only if the midpoints of the sides and the feet of the four maltitudes are eight concyclic points ; the eight ...
If the quadrilateral is a parallelogram, then the midpoints of the diagonals coincide so that the connecting line segment has length 0. In addition the parallel sides are of equal length, hence Euler's theorem reduces to + = + which is the parallelogram law.
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).
A four-sided parallelogon is called a parallelogram. ... Parallelogram: Z 2, order 2 Rectangle & rhombus: Dih 2, order 4 Square: Dih 4, order 8 6 Elongated parallelogram:
For example, in a rectangle, every maximal square not touching one of the shorter sides is a separator. A continuator square is a square s in a polygon P such that the intersection between the boundary of s and the boundary of P is continuous. A maximal continuator is always a corner square. Moreover, a maximal continuator always contains a knob.
Hutton's definitions in 1795 [4]. The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια (trapezia [5] literally 'table', itself from τετράς (tetrás) 'four' + πέζα (péza) 'foot ...