Perimeter of a Parallelogram
In this lesson, we will learn about the perimeter of a parallelogram.
About This Lesson
In this lesson, we will:
- See an example on finding the perimeter of a parallelogram.
- See another example on finding the side length of a parallelogram.
The study tips and math video below will explain more.
A parallelogram has two pairs of parallel sides and its opposite sides are equal in length. These properties are shown on the right.
Now, if the parallelogram has sides of length a and b, the perimeter of the parallelogram, P, will be:
P = 2(a+b)
This formula is similar to the formula for the perimeter of a rectangle. Rather than repeating the same explanation, the math video below will show some examples on the perimeter of a parallelogram without using the formula.
Math Video Transcript
In this lesson, we will see some examples on the perimeter of a parallelogram.
Consider this parallelogram. We can see that, these 2 parallel sides have the length of 3cm and these 2 parallel sides have the length of 5cm.
Find the perimeter of this parallelogram.
Now, to find the perimeter of the parallelogram, P, we just add the length of these sides together.
Hence, we have P, equals to 3, add with 5, add with another 3, and add with another 5.
Therefore, we have P=3+5+3+5.
Let's calculate this. 3, add with 5, gives 8. 5, add with 8, gives 13. 3, add with 13, gives 16.
Hence, we have P=16.
Now, this number has no meaning, unless we include the unit for it.
Since the side lengths are given in centimeter, the perimeter must also be in centimeter.
Hence, the perimeter of this parallelogram is 16cm.
Next example, the perimeter of this parallelogram is 30ft. Find x.
Here, we can see that, this parallelogram has 2 parallel sides of length 8 feet, and, another 2 parallel sides of length x.
Now, we can find the perimeter of the parallelogram, by adding all the side lengths together.
By doing so, we have x, add with 8, add with another x, and add with another 8.
Since the perimeter is given as 30ft, this expression must be equals to, 30.
Before we continue, let's arrange the like terms together.
Now, let's simplify this equation. 8, add with 8, gives 16.
x, add with x, gives 2x.
Now, we have 2x+16=30.
To get a step closer in finding x, we need to remove 16.
To do so, we add -16 to both sides of the equation.
By doing so, we get, 2x equals to, 30 minus 16. 30, minus 16, gives 14.
Next, to find x, we need to remove 2. We can do so, by dividing both sides of the equation with 2.
By doing so, we get, x=14/2.
14, divided by 2, gives 7. Hence, we have, x=7.
Again, this number has no meaning unless we include the unit for it.
Since, the unit is in feet, 7 will also be in feet.
Finally, we have, x=7ft.
That is all for this lesson. Try out the practice question to further your understanding.
Practice Questions & More
Multiple Choice Questions (MCQ)
Now, let's try some MCQ questions to understand this lesson better.
You can start by going through the series of questions on the perimeter of a parallelogram or pick your choice of question below.
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