In Euclidean geometry, a rhombus is a type of quadrilateral. It is a special case of a parallelogram, whose diagonals intersects each other at 90 degrees. This is the basic property of rhombus. The shape of rhombus is in diamond shape, hence it is also called a diamond. You must have seen the diamond shape in the playing cards. All the rhombus are parallelogram and kite. And if the angles of the rhombus are all 90 degrees, then it is a square.
A quadrilateral is a polygon containing 4 sides and 4 vertices enclosing 4 angles. The sum of the interior angles of a quadrilateral is equal to 360 degrees. The quadrilateral are basically of 6 types such as:
A rhombus is a special case of a parallelogram and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and opposite angles are equal. Moreover, all the sides of a rhombus are equal in length and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond. The plural form of rhombus is rhombi or rhombuses.
In the above figure, you can see a rhombus ABCD, where AB, BC, CD and AD are the sides of rhombus and AC & BD are the diagonals of a rhombus.
Rhombus has all its sides equal and so do the square. Also, the diagonals of the square are perpendicular to each other and bisect the opposite angles. Therefore, a square is a type of rhombus.
The opposite angles of a rhombus are equal to each other. Also, the diagonals of a rhombus bisect these angles.
The formulas for rhombus are defined for two major attributes such as:
The area of the rhombus is the region covered by it in a two-dimensional plane. The formula for the area is equal to the product of diagonals of rhombus divided by 2. It can be represented as:
|Area of Rhombus, A = (d1 x d2)/2 square units|
where d1 and d2 are the diagonals of rhombus.
The perimeter of rhombus is the total length of its boundaries. Or we can say the sum of all the four sides of a rhombus is its perimeter. The formula for its perimeter is given by:
|Perimeter of Rhombus, P = 4a units|
Where, the diagonals of the rhombus are d1 & d2 and ‘a’ is the side.
Some of the important properties of the rhombus are as follows:
The sample example for the rhombus is given below.
Question: The two diagonal lengths d1 and d2 of a rhombus are 6cm and 12 cm respectively. Find its area.
Diagonal d1 = 6cm
Diagonal d2= 12 cm
Area of the rhombus, A = (d1 x d2)/2 square units
A = ( 6 x 12)/2
A = 72/2
A = 36 cm2
Therefore, the area of rhombus = 36 square units.
Question 2: Find the diagonal of a rhombus if its area is 121 cm2 and length measure of longest diagonal is 22 cm.
Solution: Given: Area of rhombus = 121 cm2 and Lets say d1 = 22 cm.
Using Area of the rhombus formula, A = (d1 x d2)/2 square units, we get
121 = (22 x d2)/2
121 = 11 x d2
or 11 = d2
Question 3: What are the basic properties of rhombus?
Solution: The basic properties of rhombus are:
Question 4: What is the perimeter of rhombus whose sides are all equal to 6 cm?
Solution: Given, the side of rhombus = 6cm
Since all the sides are equal, therefore,
Perimeter = 4 x side
P = 4 x 6
P = 24 cm