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Difference Between Rhombus and Rectangle
In geometry, we have set quadrilaterals, two-dimensional shapes with four sides, four angles, and four vertices. Rhombuses and rectangles are among the common shapes seen around us. However, they seem to have a few common properties, but they have a few other properties that mark the point of differences between them. The main difference between them is that a rhombus has all equal sides, whereas, in a rectangle, the opposite sides are equal.
|1.||What is a Rhombus and a Rectangle?|
|2.||Properties of a Rhombus and a Rectangle|
|3.||Rhombus and Rectangle are Parallelograms|
|4.||Difference Between a Rhombus and a Rectangle|
|5.||Rhombus and Rectangle Formulas|
What is a Rhombus and a Rectangle?
Although rhombuses and rectangles are quadrilaterals, there are certain properties that differentiate them.
A rhombus is a two-dimensional shape and is also characterized as a special parallelogram as it fulfills the requirements of a parallelogram, a type of parallelogram with four congruent sides. It has four equal sides, with the opposite angles being equal to each other, whereas its adjacent angles are supplementary.
A rectangle is a also two-dimensional shape. It has four equal angles and four vertices. All the four angles of a rectangle measure 90°. It is also called a parallelogram as its opposite sides are parallel.
Properties of a Rhombus and a Rectangle
Some important properties of a rhombus are:
- All four sides are equal in length.
- Opposite angles are equal.
- Diagonals bisect each other.
- The Sum of any two adjacent is 180°.
Some important properties of a rectangle are:
- The opposite sides of a rectangle are equal and parallel to each other.
- All the internal angles of a rectangle measure 90°.
- The opposite angles of a rectangle are equal, hence, called a parallelogram.
- The diagonals of a rectangle are of the same length and bisect each other.
Rhombus and Rectangle are Parallelograms
A parallelogram is a two-dimensional closed shape with opposites sides being equal and parallel to each other. Also, the opposite angles are equal. The diagonals bisect each other and divide the parallelogram into two congruent triangles. A parallelogram is further divided into three special types, a rhombus and rectangle are two of them.
- A rectangle is a parallelogram with two pairs of equal and parallel opposite sides and four right angles.
- A rhombus is a parallelogram with four equal sides in which the opposite angles are equal.
Difference Between a Rhombus and a Rectangle
The important differences between a rhombus and a rectangle are listed in the table given below.
Rhombus vs Rectangle
|Sides||A rhombus has four equal sides.||In a rectangle, the opposite sides are equal.|
|Diagonals||The diagonals of a rhombus bisect each other at 90°.||The diagonals of a rectangle bisect each other at different angles. One angle is an obtuse angle and the other one is an acute angle.|
Opposite angles are equal.
Adjacent angles add up to 180°.
Diagonals make right angles at the center.
Opposite angles, as well as adjacent angles, are equal.
An angle formed by the adjacent sides of a rectangle is 90°.
Diagonals make different angles at the center - an obtuse angle and an acute angle.
|Lines of Symmetry||A rhombus has two lines of symmetry.||A rectangle also has two lines of symmetry.|
Rhombus and Rectangle Formulas
Once we know the length of the sides and the length of the diagonals of a given square and a rhombus, we can use the following formulas to calculate their area and perimeter.
- The formula used to find the area of a rhombus is: Area = 1/2×d1×d2, where d1 and d2 are the lengths of the diagonals.
- The formula used to find the perimeter of a rhombus is: Perimeter = 4 × s, where 's' is the length of the side of a rhombus.
- The formula used to find the area of a rectangle is: Area of a rectangle = l × b, where 'l' is the length of the rectangle and 'b' is the breath of the rectangle.
- The formula used to find the perimeter of a rectangle is: Perimeter = 2 (l + b), where 'l' is the length of the rectangle and 'b' is the breath of the rectangle.
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Examples on Difference Between a Rhombus and a Rectangle
Example 1: Have a look at the given properties of a parallelogram and identify if the given parallelogram is a rhombus or a rectangle.
- The opposite sides are equal to each other and the interior angles are all right angles.
- The diagonals are of equal length and bisect each other.
Although, a rhombus and a rectangle, are parallelograms only. But the properties given above are that of a rectangle as in the case of a rhombus, the interior angles are not right angles, even the diagonals are of unequal measure.
Therefore, the given parallelogram is a rectangle, not a rhombus.
Example 2: A rhombus has sides of length 4 units. Calculate its perimeter.
The formula used to calculate the perimeter of a rhombus is: perimeter = 4 × s, where 's' is the length of the side of a rhombus.
Given, side = 4 units. Substituting the values in the formula:
Perimeter = 4 × s = 4 × 4
= 16 units
Therefore, the perimeter of the given rhombus is 16 units.
Practice Questions on Difference Between Rhombus and Rectangle
FAQs on Difference Between Rhombus and Rectangle
What Is the Difference Between Rhombus and Rectangle?
The important points of differences between a rhombus and a rectangle:
- A rhombus has four equal sides, whereas, in a rectangle, the opposite sides are equal.
- The diagonals of a rhombus bisect each other at 90°, whereas the diagonals of a rectangle bisect each other at different angles.
- In a rhombus, the opposite angles are equal, whereas, in a rectangle, all angles measure 90°.
What Are the Similarities Between Rhombus and Rectangle?
A rhombus and a rectangle have the following similarities:
- The opposite angles are equal.
- The diagonals are equal in length and bisect each other.
- Their opposite sides are equal and parallel.
What Property of Rhombus Is Different from the Property of Rectangle?
The property of a rhombus that makes it different from a rectangle is as follows: A rhombus has all its four sides equal. Both the diagonals are equal and bisect each other at right angles.
How Are Rhombus and Rectangle Different in Terms of their Diagonals?
The diagonals of Rhombus are not equal in length but are perpendicular to each other at the point of intersection, whereas the diagonals of Rectangle are equal but are not perpendicular to each other at the point of intersection.
Why Is a Rhombus Never a Rectangle?
Rhombus and rectangle, both are special parallelograms but rhombuses, in general, are not rectangles, mainly because of the vertex angles, which are all right angles in the case of a rectangle.