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## Area of Rhombus

To find Area of Rhombus, multiply the lengths of the two diagonals and divide by 2 (same as multiplying by 1/2): The sides and angles of a rhombus: The sides of a rhombus are all congruent (the same length.)

Students who want to know the formula and how to Calculate Rhombus Area with Examples, Derivation they will get through below section of this page which is well structured by the team of recruitmentresult.com.

### Area of Rhombus

Rhombus Definition

A rhombus is a four sided quadrilateral where all sides have same length and its diagonals bisect each other at right angles. Opposite sides of a rhombus are parallel and opposite rhombus angles are equal. Sometimes, rhombus is also called as rhombus diamond.

Formula to Calculate Area, Perimeter, Circumference: Find Area of Circle

Properties of a Rhombus

 Base Any side can be considered a base. Choose any one you like. If used to calculate the area (see below) the corresponding altitude must be used. In the figure above one of the four possible bases has been chosen. Altitude The altitude of a rhombus is the perpendicular distance from the base to the opposite side (which may have to be extended). In the figure above, the altitude corresponding to the base CD is shown. Area There are several ways to find the area of a rhombus. The most common is (base × altitude). Each is described in Area of a rhombus Perimeter Distance around the rhombus. The sum of its side lengths. See Perimeter of a rhombus Diagonals Each of the two diagonals is the perpendicular bisector of the other. See Diagonals of a rhombus

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What Is The Formula Of Area Of Rhombus

ABCD is a rhombus whose base AB = b, DB ⊥ AC   DB = d₁ AC = d₂ and the altitude from C on AB is CE, i.e., h.

Area Of Rhombus Proof

Area of rhombus ABCD   = 2 Area of ∆ ABC

= 2 × 1/2 AB × CD sq units.

= 2 × 1/2 b × h sq. units

= base x height sq. units

Also, area of rhombus    = 4 × area of ∆ AOB

= 4 × 1/2 × AO × OB sq. units

= 4 × 1/2 × 1/2 d₂ × 1/2 d₁ sq. units

= 4 × 1/8 d₁ × d₂ square units

= 1/2 × d₁ × d₂; where d₁ and d₂ are diagonals.

Therefore, area of rhombus = 1/2 (product of diagonals) square units

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Area of the Rhombus

Let us see how to calculate the area of a rhombus. There are three types of methods to do so.

Area of Rhombus with Diagonals

Step 1. Find the length of diagonal 1, d1. It is the distance between A and C.The diagonals of a rhombus are perpendicular to each other making 4 right triangles when they intersect each other at the center of the rhombus.

Step 2. Find the length of diagonal 2, which is the distance between B and D.

Step 3. Multiply the diagonals, d1 and d2. Do square the units.

Step 4. Divide the result by 2.

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Let us see one example:

Calculate The Area

Square of side a = 2 * 2= 4 cm2

Area, A= s2 * sin (33)

A= 4 * 0.9999
A= 4 cm2 of rhombus with diagonal 1 as 6 cm and diagonal 2 as 8 cm.

Solution: Given that,

Diagonal 1, d1 = 6 cm

Diagonal 2, d2 = 8 cm

Area of a rhombus, A = (d1 * d2) / 2

= (6 * 8) / 2
= 48 / 2
= 24 cm2

Hence, Area of a rhombus is 24 cm2.

Also Get Here: Volume And Surface Area Questions And Answers

Using Base and Height

Step 1. Find the base and the height of the rhombus. The base of the rhombus is one of its sides, and the height is the altitude which is the perpendicular distance from the chosen base to the opposite side.

Step 2. Multiply the base and calculated height.

Let us see one example.

Calculate the area of a rhombus if its base is 10 cm and height is 7 cm.

Solution: Given,

Base, b = 10 cm

Height, h = 7 cm

Area, A = b * h

= 10 * 7 cm2

A= 70 cm2

Using Trigonometry

Step 1. Square the length of any of the sides.

Step 2. Multiply it by Sine of one of the angles.

Let us see one example

Calculate area of a rhombus if the length of its side is 2 cm and one of its angle A is 33.

Solution: Given,
Side a= 2 cm
Angle A=33
Square of side a = 2 * 2= 4 cm2
Area, A= s2 * sin (33)
A= 4 * 0.9999
A= 4 cm2

Area and Perimeter of Rhombus

Question 1: The side of a rhombus is 18 cm. Find its perimeter.

Solution:

Perimeter of Rhombus = 4 x side

⇒ = 4 x 18

&rArr = 72 cm

∴ Perimeter of Rhombus = 72 cm

Question2: Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.

Solution :
Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.
AC = 24 ⇒ AO = 12
Let BO = x and AB = 13 cm (given)
By Pythagorean theorem
c 2 = a 2 + b 2
13 2 = 12 2 + x 2 169 = 144 + x 2
x 2 = 169 – 144
x 2 = 25
x = 5 cm
BO = 5 cm
Diagonal BD = 2 x 5 = 10 cm.
Area = ½ x [ product of diagonals]
= ½ x 24 x 10
Area = 120 sq.cm

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# Area of Rhombus when diagonals are given

Find the area of a rhombus PQRS. The horizontal diagonal PR is 12 and the vertical diagonal QS is 26.

Solution:

Let a – The horizontal diagonal = (PR) = 12

b – The vertical diagonal = (QS) = 26

Area of a rhombus = 1/2 (a X b)

Area = 1/2 (12 X 26)

= 6 X 26

= 156 sq units.

# Area of rhombus when side and diagonal is given

Find the area of a rhombus one side of which measures 20 units and one diagonal 24 units

Solution:

Consider 1 triangle formed when both diagonals are drawn.

side ^ 2 = (1/2 diagonal 1)^2 + (1/2 diagonal 2)^2

400 = 144 + (1/2 diag 2) ^2

=> diag 2 = 32.

diag 1 = 24.

Area = 24 x 16 = 384

Get Here:  Area Of A Trapezium Formula

# Area of rhombus when side and altitude is given

Find the area of the rhombus with the given base 24 and height 10.

Solution:

Given: Base (b) = 24 and height (h) = 10

Area of a rhombus = b * h

= 24 * 10

= 240 sq units.

Final Note:

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