**Perimeter of a
Rhombus**

We know that the rhombus is a plane figure or two-dimensional figure. All the sides of a rhombus are equal. The opposite sides of a rhombus are parallel and the opposite angles are equal. Its diagonals bisect each other at 90°.

The **perimeter **of a closed
two-dimensional figure is the length of its boundary. The units of measurement
of perimeter are the same as that of length, i.e. cm, m or km.

The perimeter of a rhombus can be
found the same as the square.

To find the perimeter of a rhombus,
we add the measures of all its sides.

Let we have to find the perimeter of a given rhombus ABCD.

Perimeter of the rhombus ABCD = AB
+ BC + CD + DA

= AB + AB + AB + AB (Since, AB = BC = CD = DA)

= 4 AB

= 4 × side

Thus, the **perimeter of a rhombus
= 4 **×** side**

If the length of each side of the rhombus
is *s*, then

**Perimeter
of a rhombus =** **4 **×** s**

**Perimeter of a Rhombus
Formula**

**Perimeter
of a rhombus = 4 **×** s**

Where *s* is the length of each
side of the rhombus.

**Perimeter of a Rhombus
Example**

**Example 1: **Find
the perimeter of a rhombus, whose each side measures 7.5 cm.

**Solution: **Given:
side of the rhombus, s = 7.5 cm

Perimeter of a rhombus = 4 ×
s

= 4 × 7.5 cm

= 30 cm

**Example 2: **A
plot is in the shape of a rhombus. If each side of the plot measures 90

m, find the length of the rope
required to fence all around it 5 times.

**Solution: **Given:
length of each side of plot, s = 90 m

Length of the rope required to fence
it one time = Perimeter of the plot

= 4 × s

= 4 × 90 m

= 360 m

Length of the rope required to fence
the plot 5 times = 5 × 360 m = 1800 m

Hence, the total length of the rope
required to fence the plot is 1800 m.

**Example 3: **Rohit jogs 10 rounds of a rhombus-shaped park which is 50 m
long. Find the total distance jogged by him in kilometres.

**Solution: **Given: length of the park, s = 50 m

Distance covered by Rohit
in 1 round = Perimeter of the park

= 4 × s

= 4 × 50 m

=
200 m

Total distance covered
by Rohit in 10 rounds = 10 × 200 m = 2000 m

Thus, the total distance
jogged in kilometres = 2000/1000 km

(Since
1 km = 1000 m)

= 2 km

**Example 4: **If the perimeter of a rhombus-shaped plot is 280 m, find the
measure of each side of the plot.

**Solution: **Given: perimeter of the plot = 280
m

We know that,

Perimeter of a rhombus =
4 × s

280 m = 4 × s

s = 280/4 = 70 m

Hence, the measure of
each side of the rhombus-shaped plot is 70 m.

**Example 5: **Each
side of a rhombus-shaped photo frame measures 58 cm. If its border is 4 cm wide, then find the
perimeter of the picture.

**Solution: **Given:
Side of the photo frame = 58 cm

Each side of the picture = 58 cm – (4
cm + 4 cm) = 50 cm

Thus, the perimeter of the picture = 4
× s

= 4 × 50

= 200 cm

Hence, the perimeter of the picture is
200 cm.