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

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Test yourself on perimeter of a triangle!

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

1.51.51.5AAABBBCCCDDD9.5

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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 Triangle

Exercise #1

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

1.51.51.5AAABBBCCCDDD9.5

Video Solution

Step-by-Step Solution

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

AD=BC=9.5 AD=BC=9.5

AB=CD=1.5 AB=CD=1.5

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

1.5+9.5+1.5+9.5=19+3=22 1.5+9.5+1.5+9.5=19+3=22

Answer

22 cm

Exercise #2

Calculate the perimeter of the trapezoid according to the following data:

777101010777121212AAABBBCCCDDD

Video Solution

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

  • List the lengths of the sides: the bases are 1010 and 1212, and the two non-parallel sides are each 77.
  • Apply the perimeter formula for a trapezoid: P=a+b+c+d P = a + b + c + d .
  • Substitute the given values into the formula: P=10+12+7+7 P = 10 + 12 + 7 + 7 .
  • Calculate the sum: P=10+12+7+7=36 P = 10 + 12 + 7 + 7 = 36 .

Therefore, the perimeter of the trapezoid is 36 36 .

This matches the correct answer choice from the provided options.

Answer

36

Exercise #3

Calculate the perimeter of the trapezoid below:

999555121212444

Step-by-Step Solution

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

  • Step 1: Identify the given side lengths of the trapezoid.
  • Step 2: Use the perimeter formula for a trapezoid, which is the sum of the lengths of its sides.
  • Step 3: Perform the necessary addition to compute the perimeter.

Now, let's work through each step:
Step 1: The trapezoid has side lengths of 99, 55, 1212, and 44.
Step 2: The formula for the perimeter PP of a trapezoid is:
P=side1+side2+side3+side4 P = \text{side}_1 + \text{side}_2 + \text{side}_3 + \text{side}_4
Step 3: Plugging in the values, we compute:
P=9+5+12+4 P = 9 + 5 + 12 + 4
Step 4: Calculating the sum:
P=30 P = 30

Therefore, the perimeter of the trapezoid is 3030.

Answer

30

Exercise #4

Calculate the perimeter of the trapezoid below:

161616161616111151515

Step-by-Step Solution

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

  • Identify the given side lengths of the trapezoid.
  • Apply the formula for the perimeter of a trapezoid.
  • Perform the addition of all side lengths to calculate the perimeter.

Let's work through each step:

Step 1: Identify the given side lengths. The trapezoid has:

  • Top base: a=16 a = 16
  • Bottom base: b=1 b = 1
  • Non-parallel side: c=15 c = 15
  • Other non-parallel side: d=16 d = 16

Step 2: We'll use the formula for the perimeter of a trapezoid:

P=a+b+c+d P = a + b + c + d

Step 3: Plug in the values and perform the calculation:

P=16+1+15+16 P = 16 + 1 + 15 + 16

P=48 P = 48

Therefore, the perimeter of the trapezoid is 48 48 .

Answer

48

Exercise #5

Calculate the perimeter of the trapezoid below:

101010111111555101010

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:

  • Step 1: Identify the side lengths of the trapezoid:
    Top side =10 = 10 , Bottom side =5 = 5 , Left side =10 = 10 , Right side =11 = 11 .
  • Step 2: Apply the perimeter formula:
    The formula for the perimeter P P of a trapezoid is P=a+b+c+d P = a + b + c + d .
  • Step 3: Perform the calculations:
    Substitute the given lengths into the formula:
    P=10+5+10+11=36 P = 10 + 5 + 10 + 11 = 36 .

Therefore, the perimeter of the trapezoid is 36 36 .

Answer

36

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