Difference Between Diamond, Rhombus and Trapezoid

A Diamond, Rhombus and Trapezoid are three geometric shapes that can sometimes be confused with each other due to their similar appearances. However, they are distinct shapes with the unique properties and characteristics.

A Diamond is a type of parallelogram in which all four sides are of equal length. Additionally, opposite angles of the diamond are congruent (i.e., they have the same degree measure). Another way to the describe a diamond is as a four-sided figure with two pairs of parallel sides and no right angles. 

A Rhombus is a type of parallelogram in which all four sides are of equal length, just like a diamond. However, unlike a diamond, opposite angles of the rhombus are also congruent. In other words, a rhombus is the parallelogram in which all sides are equal but not all angles are right angles. And their diagonals intersect each other at 90 degree.

Diamond 

The diagonals are perpendicular bisectors of each other and intersect at a 90-degree angle. Let’s call the length of the diagonals “d”. 

Diamond

Find the length of each side of the Diamond:

s = √(d² / 2)

the formulas for a Diamond with diagonal length “d” are:

Area of a Diamond: A = d1 x d2 / 2 = d² / 2

Perimeter of a Diamond: P = 4 x s = 4 x √(d² / 2) 

Rhombus 

The diamond is a special case of a rhombus with a specific angle between its sides. Since a rhombus has all sides equal in length and opposite angles equal.

Rhombus

Area of a Rhombus: A = d1 x d2 / 2, where d1 and d2 are the lengths of the diagonals of the rhombus.

Perimeter of a Rhombus: P = 4 x a, where a is the length of one side of the rhombus.

 Trapezoid 

A trapezoid is a quadrilateral with two parallel sides of different lengths. It is also known as a trapezium in some parts of the world.

Trapezoid

Formula for the area of the Trapezoid is:

Area = (b1 + b2) x h / 2

where b1 and b2 are the lengths of the two bases, and h is the height of the trapezoid.

Difference Between Diamond Rhombus and Trapezoid :

Diamond	Rhombus	Trapezoid
A four-sided shape with two pairs of parallel sides where all sides are equal in length and opposite angles are equal.	four-sided shape with two pairs of parallel sides  where all sides are equal in length.	A four-sided shape with two parallel sides of different lengths.
Two opposite angles are acute and two opposite angles are obtuse	Opposite angles are congruent.	The angles at the non-parallel sides are supplementary
The diagonals are perpendicular bisectors of each other and intersect at a 90-degree angle.	Both diagonal of Rhombus bisect the vertex angles through which it passes.	The diagonals intersect at a point, but do not bisect each other.
Formula : Area = d2 / 2, where d is the length of a diagonal.	Formula : Area = (d1 * d2 ) / 2 , where the d1  is the length of diagonal 1 and d2 is the length of diagonal 2	Formula : Area = (sum of bases / 2) x height, where the bases are the parallel sides and the height is the perpendicular distance between them.