Perimeter of a Rhombus

# Perimeter of a Rhombus

## 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.