Perimeter of a Parallelogram
We know that a parallelogram
is a plane figure or two-dimensional figure. The opposite sides of a parallelogram
are parallel and equal. Its diagonals bisect each other but they are not equal
in length.
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.
To find the perimeter of a parallelogram,
we add the measures of all its sides.
Let we have to find the perimeter of a given parallelogram ABCD.
Perimeter of parallelogram ABCD =
AB + BC + CD + DA
= AB + BC + AB + BC (Since, AB = CD and BC = DA)
= 2 AB + 2 BC
= 2 (AB + BC)
= 2 (length + breadth)
Thus, the perimeter of a parallelogram
= 2 (length + breadth)
If the length is l and the
breadth is b, then
Perimeter
of a parallelogram = 2 (l + b)
Perimeter of a Parallelogram
Formula
Perimeter
of a parallelogram = 2 (l + b)
Where l is the length and b
is the breadth of the parallelogram.
Perimeter of a Parallelogram
Example
Example 1: Find
the perimeter of a parallelogram whose length and the breadth
measure 12 cm and 8 cm, respectively.
Solution: Given:
l = 12 cm and b = 8 cm
Perimeter of a parallelogram = 2
(l + b)
= 2 (12 + 8) cm
= 2 × 20 cm
= 40 cm
Example 2: A
parallelogram-shaped plot is 75 m long and 65 m wide. Find the length
of the rope required to fence all
around it.
Solution: Given:
length of the plot, l = 75 m and breadth of the plot, b = 65 m
Perimeter of a plot = 2 (l + b)
=
2 (75 + 65) m
= 2 × 140 =
280 m
Hence, the total length of the rope
required to fence the plot is 280 m.
Example 3: A soldier jogs 25 rounds of a parallelogram-shaped park which is
90 m long and 60 m wide. Find the total distance jogged by the soldiers in
kilometres.
Solution: Given: length of the park = 90 m and breadth of the park = 60 m
Distance covered by the soldiers
in 1 round = Perimeter of the park
= 2 (90
m + 60 m)
= 2 × 150 m = 300 m
Total distance covered
by the soldiers in 25 rounds = 25 × 300 m = 7500 m
Thus, the total distance
covered in kilometres = 7500/1000 km
(Since 1 km = 1000 m)
= 7.5 km
Example 4: If the perimeter of a parallelogram is 130 cm and its breadth is 30 cm, find the length of
the parallelogram.
Solution: Given: perimeter of the parallelogram = 130
cm and breadth of the parallelogram = 30 cm
We know that,
Perimeter of a parallelogram = 2
(l + b)
130 cm = 2 (l + 30)
⇒ l + 30 = 65
⇒ l = 35 cm
Hence, the length of the
parallelogram
is 35 cm.
Example 5: A
parallelogram-shapes hoarding is 170 cm long and 130 cm wide. If the
border is 10 cm wide, then find the
perimeter of the picture.
Solution: Given:
Length of the hoarding = 170 cm
Length of the picture = 170 cm – (10
cm + 10 cm) = 150 cm
Width of the hoarding = 130 cm
Width of the picture = 130 cm – (10 cm
+ 10 cm) = 110 cm
Thus, the perimeter of the picture = 2
(length + breadth)
= 2 (150 cm + 110 cm)
= 2 × 260 cm = 520 cm
Hence, the perimeter of the picture is 520 cm.