How do we calculate the perimeter of polygons?

🏆Practice perimeter of a triangle

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.

Educational chart comparing perimeter formulas of polygons—triangle, rectangle, square, parallelogram, and rhombus—with labeled orange shapes and corresponding perimeter equations

Start practice

Test yourself on perimeter of a triangle!

Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Practice more now

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.

Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Examples with solutions for Perimeter of a Triangle

Exercise #1

Calculate the perimeter of the following parallelogram:

101010888

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information
  • Step 2: Apply the appropriate perimeter formula for the parallelogram
  • Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us the lengths of two adjacent sides of the parallelogram: a=10a = 10 and b=8b = 8.
Step 2: We'll use the formula for the perimeter of a parallelogram: P=2(a+b)P = 2(a + b).
Step 3: Plugging in our values, we get:

P=2(10+8)=2×18=36 P = 2(10 + 8) = 2 \times 18 = 36

Therefore, the perimeter of the parallelogram is 3636.

Answer

36

Exercise #2

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

777121212AAABBBCCCDDD

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 #3

Given the parallelogram:

888666AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Video Solution

Step-by-Step Solution

To calculate the perimeter of the parallelogram ABCD, we need the lengths of its two adjacent sides. Given that one side, AB, is 8 units, and recalling that adjacent parallelogram sides will mirror their opposites, AC represents a relevant measurement within the context—but sides not involved with inclination describe standard periphery bounds without adjustments (hence reliance on visually positioned evaluation without contradictions).

Following the perimeter formula for parallelograms:

P=2(a+b) P = 2(a + b)

In our shape, let’s define:

  • a=8 a = 8 (Length of side AB or its opposite estimation feature equated)
  • b=6 b = 6 (Instinctive reconfirmation according to positive iteration; i.e., default parameter for spatial definition)

Plugging these values into our formula, we get:

P=2(8+6) P = 2(8 + 6) P=2(14) P = 2(14) P=28 P = 28

Therefore, the perimeter of the parallelogram is 28 28 units.

Answer

28

Exercise #4

Calculate the perimeter of the following parallelogram:

333111

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the base and side of the parallelogram from the diagram.
  • Step 2: Use the perimeter formula for a parallelogram.
  • Step 3: Substitute the values into the formula to find the perimeter.

Now, let's work through each step:
Step 1: From the diagram, the base of the parallelogram is given as 3 3 units (top side). Despite the lack of explicit vertical length values, the common approach is to assume symmetrical side lengths—both the base and the side given symmetrically leads us to a second side, typically directly inferred. However, since all clear interpretation points to utilizing 1 and horizontal 3, we verify with associated edge matching.
Step 2: Use the formula for the perimeter of the parallelogram: P=2×(base+side) P = 2 \times (\text{base} + \text{side}) .
Step 3: Substitute the given values into the formula: P=2×(3+1) P = 2 \times (3 + 1) .
Calculating this gives us: P=2×4=8 P = 2 \times 4 = 8 .

Therefore, the solution to the problem is P=8 P = 8 .

Answer

8

Exercise #5

Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Video Solution

Step-by-Step Solution

To find the perimeter of the parallelogram, we follow these steps:

  • Step 1: Identify the given side lengths from the diagram: AB=4 AB = 4 units and AD=2 AD = 2 units.
  • Step 2: Use the perimeter formula for a parallelogram, which is P=2(a+b) P = 2(a + b) .
  • Step 3: Substituting the given values into the formula: a=4 a = 4 and b=2 b = 2 .

Proceeding with the calculation:

P=2(4+2)=2×6=12 P = 2(4 + 2) = 2 \times 6 = 12 .

Therefore, the perimeter of the parallelogram is 12 units.

Answer

12

Start practice

More Questions

Related Subjects