**Area of a Rhombus**

A rhombus is a special type of parallelogram
in which all the sides are equal and the diagonals bisect each other at right
angles. To find the area of rhombus, we use the method of splitting the
quadrilateral into two triangles.

We know that the area of a triangle = ½ × base × height

Area of rhombus ABCD = Area of Î”ABC +
Area of Î”ADC

= ½ × AC × BO + ½ × AC × DO

= ½ ×
AC × (BO + DO)

= ½ × AC × BD

= ½ ×
*d*_{1} × *d*_{2}

Thus, **Area of a rhombus =
½ **×** d_{1} **×

*d*_{2}Where *d*_{1} and *d*_{2}
are the diagonals of the rhombus.

**Area of a Rhombus Formula**

**Area of a Rhombus Formula**

**Area of a rhombus = ½ **×** d_{1} **×

*d*_{2}*d*_{1} and *d*_{2 }are the diagonals of the rhombus.

**Hence, the area of a rhombus is equal
to half of the product of its diagonals.**

If the base and the altitude of a
rhombus is given, then we can find the area of a rhombus using the formula of the area of a parallelogram.

**Area of a rhombus = **** b **×

*h**b**h*_{ }are the base and the height of the rhombus, respectively.

**How to Find the Area of a Rhombus When Diagonals are Known**

**How to Find the Area of a Rhombus When Diagonals are Known**

Consider a rhombus ABCD with two diagonals AC and BD.

**Step 1:**Find the length of both the diagonals,*d*_{1}and*d*_{2}.**Step 2:**Multiply both the lengths,*d*_{1}and*d*_{2}.**Step 3:**Divide the result by 2.

The resultant value will give the area of the rhombus ABCD.

**How to Find the Area of a Rhombus When The Base and The Height are Known**

**How to Find the Area of a Rhombus When The Base and The Height are Known**

**Step 1:**Note down the lengths of the base and the height of the given rhombus. The base is one of the sides of the rhombus, while the height is the perpendicular

**Step 2:**Multiply the base and the height.

The resultant value will give the area of the rhombus.

**Solved Questions on Area of a Rhombus**

**Solved Questions on Area of a Rhombus**

**Example 1: **The
lengths of the diagonals of a rhombus are 16 cm and 20 cm. Find its area.

**Solution:**
Here, *d*_{1} = 16 cm and *d*_{2 }= 20 cm

Area of a rhombus = ½ × *d*_{1}
× *d*_{2}

= ½ × 16 × 20

= 160 sq. cm

**Example 2: **Find
the area of a rhombus, the lengths of whose diagonals are 30 cm and 40 cm.

**Solution:**
Here, *d*_{1} = 30 cm and *d*_{2 }= 40 cm

Area of a rhombus = ½ × *d*_{1}
× *d*_{2}

= ½ × 30 × 40

= 600 sq. cm

**Example 3: **The
area of a rhombus is 250 sq. cm. If one of its diagonals is 20 cm long, find
the length of the other diagonal.

**Solution:**
Here, *d*_{1} = 20 cm and *d*_{2 }= ?

Area of a rhombus = 250 sq. cm

Area of a rhombus = ½ × *d*_{1}
× *d*_{2}

250 = ½ × 20 × *d*_{2}

500 = 20 × *d*_{2}

*d*_{2} = 500/20 = 25 cm

Hence, the length of the other
diagonal is 25 cm.

**Example 4: **The
perimeter of a rhombus is 40 cm and one of its diagonals is 16 cm. Find the
length of the other diagonal. Also, find the area of the rhombus.

**Solution: **Perimeter
of the rhombus = 40 cm

Side of the rhombus = 40/4 = 10 cm

In the above figure, AB = BC = CD = AD
= 10 cm

Let the diagonal AC = 16 cm

Then, OC = AO = 8 cm

In right-angles triangle AOB,

OB^{2} = AB^{2} – AO^{2} [Using Pythagoras theorem]

OB^{2} = 10^{2} – 8^{2}

OB^{2} = 100 – 64

OB^{2} = 36

OB = 6 cm

Thus, the diagonal BD = 12 cm

Now, Area of a rhombus = ½ × *d*_{1}
× *d*_{2}

= ½ × 16 × 12

= 96 sq. cm

**Example 5: **If the base and the perpendicular height of a rhombus measure 5.5 cm and 4 cm respectively, find the area of the rhombus.

**Solution:** Here, *b* = 5.5 cm and *h*_{ }= 4 cm

Area of a rhombus = *b* × *h*

* = * 5.5 × 4

* = *22 sq. cm* *

**Example 6: **The perpendicular height of a rhombus is 6 cm. If the area of the rhombus is 27 sq. cm, find the side of the rhombus.

**Solution:** Here, *h* = 6 cm and area_{ }= 27 sq. cm

Area of a rhombus = *b* × *h*

* *27* = * *b* × 6

* b = *27/6 = 4.5 cm* *

Thus, each side of the rhombus is 4.5 cm.

**To find the area of a trapezium, a parallelogram, a square, a rectangle and a circle, click the following links:**