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Thus denoting the common side as a and the diagonals as p and q, in every rhombus 4 a 2 = p 2 + q 2 . {\displaystyle \displaystyle 4a^{2}=p^{2}+q^{2}.} Not every parallelogram is a rhombus, though any parallelogram with perpendicular diagonals (the second property) is a rhombus.
where K is the area of a convex quadrilateral with perimeter L. Equality holds if and only if the quadrilateral is a square. The dual theorem states that of all quadrilaterals with a given area, the square has the shortest perimeter. The quadrilateral with given side lengths that has the maximum area is the cyclic quadrilateral. [43]
Johannes Kepler in Harmonices Mundi (1618) named this polyhedron a rhombicosidodecahedron, being short for truncated icosidodecahedral rhombus, with icosidodecahedral rhombus being his name for a rhombic triacontahedron.
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 golden rhombus is a rhombus whose diagonals are in proportion to the golden ratio, ... Its area, in terms of ... in terms of side ...
A formula for the area K of a cyclic orthodiagonal quadrilateral in terms of the four sides is obtained directly when combining Ptolemy's theorem and the formula for the area of an orthodiagonal quadrilateral. The result is [11]: p.222 = (+).
It's a classic tale: You have last-minute guests coming over for dinner or a bake sale fundraiser you didn't find out about until the night before—and now you need to concoct some tasty treats ...
The definition of lozenge is not strictly fixed, and the word is sometimes used simply as a synonym (from Old French losenge) for rhombus. Most often, though, lozenge refers to a thin rhombus—a rhombus with two acute and two obtuse angles, especially one with acute angles of 45°. [ 2 ]