Perimeter of a Parallelogram

# Perimeter of a Parallelogram

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)

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.