Lozenge
Lozenge
An equilateral parallelogram whose acute angles are 45 degrees. Sometimes, the restriction to 45 degrees is dropped, and it is required only that two opposite angles are acute and the other two obtuse. The term rhombus is commonly used for an arbitrary equilateral parallelogram.
The area of a lozenge of side length a is
| A=1/2sqrt(2)a^2, |
(1)
|
its diagonals have lengths
p = sqrt(2-sqrt(2))a
(2)
q = sqrt(2+sqrt(2))a,
(3)
and it has inradius
| r=1/4asqrt(2). |
(4)
|
See also
Kite, Parallelogram, Quadrilateral, RhombusExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Lozenge." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Lozenge.html