The Formula For A Rhombus

Rhombus is a special type of Parallelogram which is of huge importance. In a rhomb, all four sides are equal and contrary pairs of lines are congruent, also opposite angles in a rhomb are equal. Rhombus often gets dislocated with square merely Rhombus is very different from the square. Why a rhombus is not considered a square is explained here. Area of the Rhombus is the space occupied by the boundaries of the Rhombus in ii-D space. Surface area of the Rhomb tin be calculated using various methods some of which are discussed in this commodity.

What is Expanse of a Rhombus?

Area of the rhomb is considered as the space enclosed past the Rhomb in the 2-D plane. It depends on the dimensions of the rhomb. It is measured in square units, such as square meters, square centimeters, etc. Area of Rhombus is measured using the formulas listed beneath

Expanse of Rhombus Formula

Expanse of the rhombus tin can be found using various methods some of them are listed in the tabular array beneath

Formulas for finding the Area of Rhombus
If Base and Height are given	A = b × h
If Diagonals are given	A = ½ × D × d
If Base and Interior angle is given	A = b² × Sin(a)

Where,

D = length of first diagonal
d = length of 2nd diagonal
b = length of side of rhombus
h = summit of rhomb
a = measure out of an interior angle

Area of Rhombus Formula

Derivation of Expanse Formula for Rhomb

Permit united states of america consider a rhomb ABCD with O equally the point of intersection of ii diagonals AC and BD.

Derivation for Rhombus Area Formula

The area of rhombus will exist

Expanse = 4 × area of △AOB

= 4 × (one/2) × AO × OB sq.units

= four × (one/ii) × (1/2) d₁× (i/two) d₂ sq.unit

= 4 × (1/eight) d_ane × d₂

= i/two d₁ × d₂

Therefore, the area of a rhomb is A = 1/2 d_ane × d_ii.

How to Find the Expanse of a Rhombus?

The area of a rhombus is the total space covered or enclosed by the rhombus on a 2-dimensional plane. The area of the rhombus tin can be calculated past three unlike methods by using diagonal, using base and meridian, and using trigonometry.

Different methods for finding surface area of Rhombus are given below

Expanse of Rhombus using Diagonal

Area = (d₁ × d₂)/two sq. units

Where,

d_ane is the length of diagonal i

d₂is the length of diagonal 2

Case one: Find the area of a rhombus having diagonals 16 m and xviii grand.

Solution:

Diagonal i, d_i= xvi m

Diagonal ii, d_ii= 18 m

Area of a rhombus, A = (d₁ × d_ii) / 2

= (16 × xviii) / 2

= 288 / 2

= 144 gⁱⁱ

Thus, the area of the rhombus is 144 m²

Area of Rhombus using Base and Superlative

Surface area of a Rhombus = b × h sq units

Where,

b is the length of whatsoever side of the rhombus

h is the tiptop of the rhombus

Case ii: Find the area of a rhombus having base of 12 chiliad and superlative is xvi thou.

Solution:

Base, b = 12 thousand

Height, h = xvi m

Area, A = b × h

= 12 × 16 m²

A = 192 m²

Thus, the area of the rhombus is 192 thousand²

Area of Rhombus using Trigonometric Ratios

Area of a Rhombus = b² × sin(A) sq. units

Where,

b is the length of any side of the rhomb

A is a measure out of any interior bending

Example 3: Find the expanse of a rhombus if the length of its side is 12 m and one of its angles A is sixty°

Solution:

Side = s = 12 thou

Angle A = 60°

Area = sⁱⁱ × sin (60°)

A = 144 × √3/2

A = 72√3 yard²

Solved Examples on Area of Rhomb

Example one: Calculate the area of a rhomb (using base and elevation) if its base is 5cm and peak is 3cm.

Solution:

Given,

Base (b) = 5cm

height of rhomb(h) = 3cm

Now,'

Expanse of the rhombus(A) = b × h

= 5 × 3

= 15cm²

Case 2: Calculate the area of a rhombus (using diagonal) having diagonals equal to 4cm and 3cm.

Solution:

Given,

Length of diagonal 1 (d1) = 4cm

Length of diagonal two (d2) = 3cm

At present,

Area of Rhombus (A) = 1/two d1 × d2

= iv x3/2 = 6cmⁱⁱ

Instance three: Calculate the expanse of the rhombus (using trigonometry) if its side is 8cm and one of its angles A is 30 degrees.

Solution:

Side of the rhombus (b) = 8cm

angle (a) = 30 degrees

Now,

Area of the rhombus(A) = b² × sin(a)

= (8) × sin(30)

= 64 × one/2 = 32 cm²

Example 4: Summate the base of a rhombus if its area is 25cm^two and tiptop is 10cm.

Solution:

Given,

Expanse = 25 cmⁱⁱ

height of rhombus(h) = x cm

At present,

Area of the rhombus(A) = b × h

25 = b × 10

= 2.v cm

FAQs on Area of Rhombus

Question i: What practise we mean past Rhomb?

Answer:

A rhomb is a type of quadrilateral whose opposite sides are parallel and equal. Also, the opposite angles of a rhombus are equal and the diagonals bisect each other at right angles.

Question ii: Give the Formula for finding the Area of a Rhombus.

Answer:

For finding the area of a rhombus, the given formula is used:

A = ½ × d₁ × d_two

where, d_i and d₂are diagonals of rhombus

Question three: How to calculate the perimeter of a rhomb?

Solution:

The perimeter of a rhomb tin can be calculated by the formula

P= 4b units

where b is a side of the rhomb.

Question 4: How to Observe the Surface area of a Rhombus When the Side and Height are Given?

Reply:

The area of a rhombus its tiptop and side are given is calculated using

A = Base × Acme sq units

Question v: Can area of a rhombus exist same equally the surface area of a square?

Answer:

No, The area of a rhombus is not the same every bit the area of a square. The area of a square is the square of its side, whereas the area of a rhombus is the half the product of diagonal i and diagonal two.

Question 6: Write the Difference between Area of Rhombus and Perimeter of Rhombus.

Answer:

Perimeter of a rhombus is the measure of its purlieus and it is calculated by adding the length of all its sides i.e. Perimeter = 4 × sides, whereas area of Rhombus is the production of its base of operations and superlative, i.e., Area = base × height.