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.
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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.
The diagonals are perpendicular bisectors of each other and intersect at a 90-degree angle. Let’s call the length of the diagonals “d”.
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)
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.
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.
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.
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.
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.
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Diamond, Rhombus vs Trapezoid
Diamond, Rhombus, and Trapezoid are all quadrilaterals, which are polygons with four sides. While rhombus and trapezium are properly defined in mathematics, diamond (or diamond shape) is a layman’s term for rhombus.
Rhombus and Diamond
A quadrilateral with all sides equal are in length is known as a rhombus. It is also named as an equilateral quadrilateral. It is considered to have a diamond shape, similar to the one in the playing cards. Diamond shape is not a precisely defined geometrical entity.
Rhombus is a special case of the parallelogram. It can be considered as a parallelogram with equal sides. The square can be considered as a special case of the rhombus, where the internal angles are right angles. In general, a rhombus has the following special properties
• All four sides are equal in length. (AB=DC=AD=BC)
• The diagonals of the rhombus bisect each other at right angles; diagonals are perpendicular to each other,
in addition to the following properties of a parallelogram.
• Two pairs of opposing angles are equal in size. (DÂB = BĈD, A ̂DC=A ̂BC)
• The adjacent angles are supplementary DÂB+A ̂DC = A ̂DC+B ̂CD = B ̂CD+A ̂BC = A ̂BC+D ̂AB = 180° = π rad
• A pair of sides, which are opposing each other, is parallel and equal in length. ( AB=DC & AB∥DC)
• The diagonals bisect each other (AO=OC, BO=OD)
• Each diagonal divides the quadrilateral into two congruent triangles. (∆ADB ≡ ∆BCD, ∆ABC ≡ ∆ADC)
• The diagonals bisect the two opposite internal angles.
Area of the rhombus can be calculated using the following formula.
Area of rhombus = ½ (AC × BD)
Trapezoid (Trapezium)
Trapezoid is a convex quadrilateral where at least two sides are parallel and unequal in length. The parallel sides of the trapezoid are known as the bases and the other two sides are called the legs.
Following are main characteristics of trapezoids;
• If the adjacent angles are not on the same base of the trapezoid, they are supplementary angles. i.e. they add up to 180° (BA ̂D+AD ̂C = AB ̂C+BC ̂D = 180°)
• The two diagonals of the trapezium intersect at the same ratio (ratio between the section of the diagonals are equal).
• If a and b are bases and c,d are legs, the lengths of the diagonals are given by
Area of the trapezoid can be calculated using the following formula.
Read the Difference Between Parallelogram and Trapezoid
What is the difference between Diamond, Rhombus and Trapezoid?
• Rhombus and Trapezoid are well-defined mathematical objects while diamond shape is a layman’s term. Each shape has four sides, and diamond shape refers to a rhombus.
• Rhombus has equal sides, with opposing sides parallel to each other. Trapezoid has unequal sides in general, with two sides parallel to each other. Only the legs of the trapezoid can be equal.
• Any diagonal of the rhombus separates the rhombus into two congruent triangles. The triangles formed by the diagonals of the trapezoid are not necessarily congruent.
• Diagonals of the rhombus intersect each other at right angles while diagonals of the trapezoid are not necessarily perpendicular to each other.
• Diagonals of the rhombus bisect each other while diagonals of the rhombus intersect at the same ratio.
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