# Questions: Area of Rhombus

In this post we will discuss some solved questions of Area of Rhombus questions. The questions are solved step by step so that you understand the concept better.

## Properties of Rhombus

Before solving questions let us understand some properties of rhombus, this will help us to understand the concept better.
Rhombus is basically a quadrilateral whose:
a. All sides are equal (AS)
b. Opposite Sides are parallel (OS)

c. Opposite angles are equal (OA)
you can remember the above property by recalling that in rhombus AS,OS and OA are equal, in this way you won’t forget its specifications.

### What is the shape of Rhombus?

Now coming to the shape of the Rhombus, it basically looks like a diamond or Kite. If you remember the shape of a kite from your childhood days you will find that it resembles the shape of Rhombus.

Some other properties of Rhombus are:

1. In Rhombus, diagonals bisect each other into equal length

2. The diagonal bisect each other at right angle
You can see from above that the diagonal are forming 4 right triangles which are concurrent to each other. The triangles are POQ, QOR, ROS, POS. All the triangles are right angled triangles.

3. The diagonals bisect the angles of rhombus

4. The sum of two adjacent angles of diagonal is 180

So the consecutive angles of Rhombus is supplementary .
Hence
Angle P + Angle Q = 180 degree
Angle Q + Angle R = 180 degree
Angle R + Angle S = 180 degree
Angle S + Angle P = 180 degree

5. Opposite angle of Rhombus are congruent
Taking note from above figure, we get
Angle P = Angle R
Angle Q = Angle S

6. Rhombus is basically a type of square as
a. Its all sides are equal
b. Diagonal bisect each other an are perpendicular
The difference is that in rhombus the adjacent sides may not be perpendicular to each other

7. When you join the midpoint of the sides of rhombus, you will get a rectangle.
The length and Breadth of rectangle will be half of the main diagonal, so the area of rectangle will be half of the area of rhombus. Let us see the figure below for full understanding of the concept.

## Important Formula for Rhombus

Some of the formulas used for solving Rhombus Problems are:
Area of Rhombus = 1/2 * d1* d2 (when diagonals are given)

Area of Rhombus = Base * Height (when base and height are given)

Perimeter of Rhombus = 4 * Side

Try to remember these formulas as you have to use it again and again while solving questions related to this topic.

## Calculate Area of Rhombus

We know that
Area of Rhombus = 1/2 * d1 * d2
where d1 and d2 are the diagonal of rhombus

In the question, one diagonal is given 48 cm
We have to find the length of other diagonal

For calculating diagonal, first you have to understand that diagonal of rhombus are perpendicular bisector of each other.
So we will take Triangle DCB and apply Pythagoras theorem

{ OC }^{ 2 }=\ { D }C^{ 2 }-{ OD }^{ 2 }\\\ \\ { OC }^{ 2 }=\ 26^{ 2 }-{ 24 }^{ 2 }\\\ \\ { OC }^{ 2 }=\ (26-24)\quad *\quad (26+24)\\\ \\ { OC }^{ 2 }=\quad 100\\\ \\ OC\quad =50\\ \\

Now as diagonals of rhombus are perpendicular bisector
So, AC ==> 2 * OC
AC ==> 100 cm

Now we got length of both the diagonals of rhombus
Area of rhombus = 1/2 * 100 * 48 ==> 2400 sq cm

Hence 2400 sq cm is the required area of Rhombus

Length of one diagonal is given d1 = 10 cm
Area of rhombus is given = 150 sq cm

We have to find the length of other diagonal of rhombus

We know that the formula of area of Rhombus is
Area of Rhombus = 1/2 * d1 * d2

==>150 = 1/2 * 10 * d2

==> d2= 300/10

==> d2= 30 cm

Hence the length of other diagonal is 30 cm

Let ABCD is a Rhombus
AC and BD are its diagonal denoted as d1 and d2

Its given that one diagonal is double of another
so, d1= 2 * d2

we know that formula for area of rhombus is
Area = 1/2 * d1 * d2

Putting the value of d1 in the area equation

Area of Rhombus = (1/2) * 2 * d2 * d2
==> 25 = d2 * d2
==> 25 = \ d2^{ 2 }
==> d2 =5

The other diagonal is twice the length
so d1=10 cm

Now we have to find the sum of diagonal d1 + d2
d1 + d2 ==> 10 + 5 ==> 15 cm
Hence 15 cm is the right answer

Let ABCD is a rhombus
The perimeter of rhombus is 56
and height is 5 meter

The perimeter of rhombus is = 4 * side
==> 56 = 4 * side
==> Side = 56/4
==> Side = 14 meter

Area of Rhombus = Base * height ==> 14 * 5 => 70 sq meter

Hence the area of rhombus is 70 sq m