Rhombus Definition
Rhombus is a quadrilateral in which all sides are equal with parallel opposite sides and equal opposite angles
Keyword for Rhombus
(a) All equal sides
(b) Opposite sides parallel
(c) Opposite angle equal
Structure of Rhombus
Important elements of Rhombus are
(a) Sides
Rhombus has four sides of equal length
AB = BC = CD = DA
(b) Angles
It has four angles
In Rhombus, opposite angles are equal
i.e. ∠A = ∠C and ∠D = ∠B
(c) Vertex
The point where two sides join is called vertex.
Rhombus has 4 vertex
Point A, B, C & D are the vertex in above figure
(d) Shape
Rhombus looks like a diamond or a star
Properties of Rhombus
(01) All sides are equal
In the above Rhombus ABCD;
AB = BC = CD = DA
All the sides have equal length
(02) Opposite sides are parallel
Observe the above image in property 01
Here side AB is parallel to CD and side DA is parallel to CB
AB || CD and DA || CB
(03) In Rhombus, opposite angles are equal
In the above image of Rhombus:
∠A = ∠C = 100 degree
∠B = ∠D = 80 degree
Both set of opposite angles are equal
(04) In Rhombus adjacent angles are supplementary
It means that sum of adjacent angles will add to 180 degree
∠A + ∠B = 180 degree
∠B + ∠C = 180 degree
∠C + ∠D = 180 degree
∠D + ∠A = 180 degree
(05) Diagonals of Rhombus bisect each other at right angle
The property is similar to square
Given above is the Rhombus ABCD with diagonals AC and BD
The diagonals bisect each other. This means that diagonals divide each other into equal halves.
i.e. AO = OC & DO = OB
Also diagonals intersect each other at right angles
(06) Diagonals also divides the angle into equal halves
Given above is the rhombus ABCD with diagonal AC
The diagonal divides the angle A & C into two equal halves.
Hence,
∠1 = ∠2
∠3 = ∠4
(07) Perimeter of Rhombus
Perimeter is the length of total boundary of any geometrical figure
Formula for Perimeter of Rhombus is:
Perimeter = Side + Side + Side + Side
Perimeter = 4 x Side
(08) Area of Rhombus
Area of Rhombus = (1/2) x d1 x d2
Where d1 & d2 are the lengths of the diagonal
(09) Making rectangle inside the rhombus
On joining the midpoint of the side of Rhombus, you will get a rectangle
ABCD is a Rhombus and P, Q, R & S are the midpoint of the respective points.
On joining the points P, Q, R and Q we get a rectangle
(10) Rhombus inside Rhombus
If you join the midpoint of half the diagonal you will get another Rhombus
ABCD is a Rhombus and AC and BD are its diagonals
AO is half of diagonal AC & P is midpoint of AO;
Similarly, R is the midpoint of OC;
Q & S are midpoints of OB & OD respectively;
On joining all the points P, Q, R & S you get another Rhombus PQRS
Frequently Asked Questions – Rhombus
(01) Are all squares a form of Rhombus?
Yes!!
In every square
(a) All sides are equal
(b) Opposite sides are parallel
(c) Opposite angles are equal
Hence, all squares can be called Rhombus
(02) Are all Rhombus a form of square?
NO!!
In Rhombus each angles may or may not be 90 degree.
Hence, all Rhombus doesn’t fulfill the requirement of Square
(03) Are all angles in a Rhombus equal?
NO!!
In a Rhombus, only opposite angles are equal
(04) What are the main difference between Rhombus and Parallelogram?
In Rhombus all sides are equal.
In Parallelogram, only opposite sides are equal
Rhombus looks like a star while parallelogram looks completely different
Solved Questions – Rhombus
(01) The length of two diagonal of Rhombus are 4 cm and 6 cm. Find the area of Rhombus
Solution
We know that:
Area of Rhombus = (1/2) x d1 x d2
Putting the value of both the diagonals in the formula
Area of Rhombus = (1/2) x 4 x 6 = 12 sq. cm
Hence, 12 sq. cm is the required area
(02) Find the perimeter of rhombus of side 5 cm
Solution
Perimeter of Rhombus = 4 x (side)
Putting the value of side length ,we get;
Perimeter of Rhombus = 4 x 5 = 20 cm
Hence, 20 cm is the required perimeter of the Rhombus
(03) If the area of Rhombus is 40 sq. cm and length of one diagonal is 8 cm. Find the length of other diagonal
Solution
Given
Area of Rhombus = 40 sq. cm
Diagonal length (d1) = 8 cm
To find
Diagonal Length (d2) = ?
We know that:
Area of Rhombus = 1/2 x d1 x d2
Putting the values in the formula, we get;
40 = (1/2) x 8 x d2
80 = 8 x d2
d2 = 80/8
d2 = 10 cm
Hence, length of other diagonal is 10 cm
(04) Given below is the Rhombus ABCD, where ∠A = 77 degree
Find the measurement of ∠B
In Rhombus, alternate angles are supplementary
∠A + ∠B = 180
77 + ∠B = 180
∠B = 180 – 77
∠B = 103 degree
Hence ∠B measures 103 degree
Summary of Rhombus Properties
