Calculating the Perimeter of a Parallelogram does not require a lot of math work. However, it is essential to know the shape and differences from other similar shapes. The reason for establishing these differences is because Polygons are similar.
The Parallelogram is very similar to the rectangle and has the same perimeter formula as the latter. Their differences are mostly only pronounced when their Areas ae being calculated. However, since the scope of this study is on Parallelogram perimeter, efforts will be made to distinguish the two shapes as much as possible.
This article will generally consider the Perimeter of the Parallelogram, the difference between t and the rectangle, and several examples to teach students.
What is the Parallelogram?
The Parallelogram is a polygon like a rectangle, triangle and trapezoid. It is a 2-dimensional shape that is extremely similar to a rectangle. It has two long parallel sides and two parallel short sides like the rectangle. Its major difference from the rectangle is that it has unequal adjacent sides meaning that its diagonals are not equal. The rectangle has similar diagonals that form a 900 at each extreme end.
Below are the two shapes, their similarities and differences.
The similarities of the shapes are that their parallel sides are equal. However, the difference in the shapes is that; while diagonals are the same in the rectangle, they vary in the Parallelogram. As can be seen from the shapes, the similarities and differences hold.
Perimeter of a Parallelogram
The Perimeter of the Parallelogram is the sum of all its sides and base. It is mathematically given as;
Perimeter = 2 (s + B)
Where;
S denotes the side of the perimeter. It is any of the two longer vertical sides of the shape.
B denotes the base of the Parallelogram. It is the horizontal part of the shape and often the shorter sides.
How to Calculate the Perimeter of a Parallelogram?
Below are the steps to calculate the Parallelogram
Step 1: identify the side and the base
Step 2: Use the Perimeter formula, which is given as; P = 2(S + B)
Calculating the Perimeter of a Parallelogram with Examples
This section will consider some examples to outline how the Parallelogram Perimeter
Example 1
Identify the shape below and calculate the perimeter
Solution
Obviously, the above shape meets all the conditions of a parallelogram and will be identified as such. Now the calculations of the perimeter will be next
The formula for the Perimeter of the Parallelogram is;
Perimeter = 2 (s + B)
Where;
S denotes the side of the perimeter
B denotes the base of the Parallelogram.
Step 1: identify the side and the base
S = 16 cm, B = 7 cm
Step 2: Use the Perimeter formula which is given as; P = 2(S + B)
P = 2 (16 cm + 7 cm)
P = 2(23 cm)
P = 46 cm
Therefore, the perimeter of the above Parallelogram with sides of 16 cm and Bases of 7 cm is 46 cm
Example 2
Consider a parallelogram with sides of 100 mm and bases of 50 mm. find the perimeter
Solution
The perimeter of the Parallelogram is given as;
P = 2 (S + B)
Since S = 100 mm and B = 50 mm then;
P = 2 (100 mm + 50 mm)
P = 2 (150 mm)
P = 300 mm
The perimeter is 100 mm. However, since perimeters of shapes are usually expressed in centimeters (cm) as opposed to millimeters (mm), it is best to convert mm to cm. that will therefore make;
P = 300 mm = 30 cm
P = 30 cm
Note that this is only necessary if a tutor or exam instruction requires that the standard unit of measurement be maintained.
Example 3
The Perimeter of a parallelogram of 56 cm while the sides is 17 cm. find the Base
Solution
P = 2 (S + B)
Where P = 56 cm, S = 17 cm and B = ?
So B is the missing value
56 cm = 2 (17 cm + B)
56 cm = 34 cm + 2B
56 cm – 34 cm = 2B
22 cm = 2B
B = 11 cm
Therefore, the Base is 11 cm.
Conclusion
The perimeter of the Parallelogram is very simple to compute and does not require any type of special or technical instruction. The calculation is very similar to that of the rectangle and abasically requires several steps to compute.
This article considered the differences between the Parallelogram and the rectangle to help students know their distinctions despite having the same basic formulas. The parallelogram perimeter was also computed using three different examples so that students could have a very good understanding of it. Just like other shapes, the perimeter of the Parallelogram can also be used to find the side or base of the shape if it is provided and one of the two is missing.
