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Ever saw a diamond? Flip it to an angle of 
, it takes a new shape. We call that shape Rhombus. Rhombus might look similar to other geometrical shapes but don't let that misguide you. It has similarities but it also has differences too. Mathematicians look at the difference and similarities and they decided that this shape should be separated from other geometrical shapes, giving it a name, Rhombus.
Rhombus and its Properties
The word, "Rhombus" is a Greek word, rhómbos, that means "a spinning top". The description of the word is the shape of a "bullroarer" which is an object whirled on a string to make a roaring noise. It comes in the category of quadrilateral because it has four sides. Other names of the rhombus are diamond, lozenge, slanting square, and equilateral quadrilateral. Below is the shape of a rhombus.
Properties of a Rhombus
A rhombus has four equal sides and equal opposite angles. The diagonals of a rhombus are perpendicular and the bisectors of the angles. Since there are two perpendicular bisectors, the angle between both bisectors will be . Furthermore, the altitude of the rhombus is the distance at right angles to two sides. Each bisector will break the rhombus into two equilateral triangles.
Area of a Rhombus
The area of a rhombus is pretty straightforward like triangle, square, rectangle, etc. The area of a rhombus is equal to the length of the larger diagonal multiplied by the smaller diagonal, divided by two.
where,
D represents the larger diagonal,
and d represents the smaller diagonal.
Perimeter of a rhombus
If you learn how to calculate area then finding the perimeter of a rhombus is easier. Rhombus has all four sides equal, all you need to do is to add all those lengths. Like area, the perimeter of the rhombus is:
Difference Between Rhombus and Parallelogram
Although rhombus shape is similar to many shapes such as diamond, square, triangle, and a few more. The most similar geometrical shape is the parallelogram. Many students often confuse rhombus with parallelogram and that is wrong.
Geometry and Area Comparision
The biggest difference between a rhombus and a parallelogram is that a parallelogram has opposite sides equal, however, a rhombus has all four sides equal like a square. Furthermore, there is a difference between the area formula for both shapes. The area of a rhombus is half of the product of large diagonal and small diagonal. On the other hand, the area of the parallelogram is the product of base and height.
Perimeter and Triangle Formation Comparision
Talking about the area, there is a big difference in perimeter too. The perimeter of the rhombus is 4 times the length but the perimeter of the parallelogram is two times the sum of its parallel lengths. Not to mention that the bisectors cut each other at a right angle in the rhombus and form two scalene triangles, but in the case of a parallelogram, the bisectors create congruent triangles and variable angles that are equal to the opposite.
Examples
Find the area and perimeter of a rhombus whose diagonals are 
and 
, and its side measures 
.
Calculate the side of a rhombus, knowing that the diagonals are and .
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I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html