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.