How do we calculate the perimeter of polygons?

🏆Practice perimeter of a parallelogram

How do we calculate the perimeter of polygons?

As long as we are dealing with a shape characterized by straight lines, the perimeter calculation will be performed by adding together all of the side lengths. This is a simple arithmetic operation that does not require any special skills. For example:

The perimeter of a shape with sides of 5, 9, 4, 6 and 7, will be 31. All you need to do is simply add up all of the sides.

Why can such a question be challenging? Owing to the fact that in tests, they don't want to examine you on arithmetic operations like addition, but rather on your proficiency in the properties of specific shapes. Therefore, you need to know the properties of polygons as they are.

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Test yourself on perimeter of a parallelogram!

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Calculate the perimeter of the trapezoid below:

101010111111555101010

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Geometry problems require you to answer various questions:

  • What is the perimeter of a shape.
  • Calculating the area of a shape.
  • Finding the length of a side and more...

How do we calculate the perimeter of polygons?

As long as we are dealing with a shape characterized by straight lines, the perimeter calculation will be performed by adding together all of the side lengths. This is a simple arithmetic operation that does not require any special skills. For example:

The perimeter of a shape with sides of 5, 9, 4, 6 and 7, will be 31. All you need to do is add up all the sides.

Why can such a question be challenging? Owing to the fact that in tests, they don't want to examine you on arithmetic operations like addition, but rather on your proficiency in the properties of specific shapes. Therefore, you need to know the properties of polygons as they are.

Example: Calculating the perimeter of a parallelogram

For example, you may encounter a question as seen below.

Given a parallelogram with sides of 5 and 6, determine the perimeter of the parallelogram.

In order to correctly answer this question, you need to know the properties of a parallelogram. We know that parallel sides in a parallelogram are equal, thus you can conclude that the length of the other sides are 5 and 8. Therefore, the perimeter of the parallelogram in this case will be 26 (5 + 8 + 5 + 8).

Additional examples:

Question: Given an isosceles triangle with a perimeter of 48. Leg a = 12. Determine the value of the base?
Answer: Given that this is an isosceles triangle, leg b is also equal to 12. Therefore, the base equals 24. (12+12 = 24)

Question: Given an isosceles triangle with a base of 26. The length of side a is 8. What is the perimeter of the triangle?
Answer: Since the triangle is isosceles, side b is also equal to 8. Therefore, the perimeter is 8 + 8 + 26 = 42.

Question: Given an equilateral triangle with side a equal to 9. What is the perimeter of the triangle?
Answer: Since the triangle is equilateral, all sides are equal. Therefore, the perimeter of the triangle is 27.

Question: Given a rectangle with adjacent sides of length 7 and 9. Determine the perimeter of the rectangle?
Answer: Since in a rectangle opposite sides are equal, we can conclude that the other sides are equal to 7 and 9. Therefore, the perimeter of the rectangle is 32.

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Examples with solutions for Perimeter of a Parallelogram

Exercise #1

101010777AAABBBDDDCCC

Calculate the perimeter of the given parallelogram.

Video Solution

Step-by-Step Solution

As is true for a parallelogram each pair of opposite sides are equal and parallel,

Therefore it is possible to argue that:

AC=BD=7 AC=BD=7

AB=CD=10 AB=CD=10

Now we can calculate the perimeter of the parallelogram by adding together all of its sides:

10+10+7+7=20+14=34 10+10+7+7=20+14=34

Answer

34

Exercise #2

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Calculate the perimeter of the given parallelogram:

Video Solution

Step-by-Step Solution

As is true for a parallelogram every pair of opposite sides are equal:

AB=CD=6,AC=BD=4 AB=CD=6,AC=BD=4

The perimeter of the parallelogram is equal to the sum of all sides together:

4+4+6+6=8+12=20 4+4+6+6=8+12=20

Answer

20

Exercise #3

Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.

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Video Solution

Step-by-Step Solution

First we need to remember that pairs of opposite sides in a parallelogram are parallel and equal.

Therefore, AB is parallel to CD and BC is parallel to AD.

From this we can conclude that AB = CD = 7.

Also: BC = AD = 12.

Finally we can calculate the perimeter by adding all the sides together:

7+7+12+12=14+24=38 7+7+12+12=14+24=38

Answer

38

Exercise #4

Look at the rectangle below:

AAABBBCCCDDD107

Calculate its perimeter.

Video Solution

Step-by-Step Solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

AB=CD=10 AB=CD=10

BC=AD=7 BC=AD=7

Now let's add all the sides together to find the perimeter of the rectangle:

10+7+10+7=20+14=34 10+7+10+7=20+14=34

Answer

34

Exercise #5

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
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Video Solution

Step-by-Step Solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

AB=CD=2 AB=CD=2

AD=BC=7 AD=BC=7

Now we can add all the sides together and find the perimeter:

2+7+2+7=4+14=18 2+7+2+7=4+14=18

Answer

18 cm

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