Examples with solutions for Perimeter of a Trapezoid: Applying the formula

Exercise #1

What is the perimeter of the trapezoid in the figure?

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Video Solution

Step-by-Step Solution

To find the perimeter we will add all the sides:

4+5+9+6=9+9+6=18+6=24 4+5+9+6=9+9+6=18+6=24

Answer

24

Exercise #2

Look at the trapezoid in the diagram.

101010777121212777

What is its perimeter?

Video Solution

Step-by-Step Solution

In order to calculate the perimeter of the trapezoid we must add together the measurements of all of its sides:

7+10+7+12 =

36

And that's the solution!

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

Exercise #6

Look at the trapezoid in the figure.

The long base is 1.5 times longer than the short base.

Find the perimeter of the trapezoid.

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Video Solution

Step-by-Step Solution

First, we calculate the long base from the existing data:

Multiply the short base by 1.5:

5×1.5=7.5 5\times1.5=7.5

Now we will add up all the sides to find the perimeter:

2+5+3+7.5=7+3+7.5=10+7.5=17.5 2+5+3+7.5=7+3+7.5=10+7.5=17.5

Answer

17.5

Exercise #7

Given an isosceles trapezoid, calculate its perimeter

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Video Solution

Step-by-Step Solution

Since this is an isosceles trapezoid, and the two legs are equal, we can state that:

AB=CD=6 AB=CD=6

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

6+6+10+12= 6+6+10+12=

12+22=34 12+22=34

Answer

34

Exercise #8

If X=3

Calculate the perimeter of the trapezoid

XXX101010X+1X+1X+16+X6+X6+XAAABBBCCCDDD

Video Solution

Step-by-Step Solution

To calculate the perimeter, we add up all the sides:

10+x+(6+x)+(x+1) 10+x+(6+x)+(x+1)

Now, given that x equals 3, we substitute in the appropriate places:

10+3+(6+3)+(3+1)= 10+3+(6+3)+(3+1)=

10+3+9+4= 10+3+9+4=

13+13=26 13+13=26

Answer

26

Exercise #9

Calculate the perimeter of the trapezoid below:

6669.879.879.8714.5214.5214.524.14.14.1

Step-by-Step Solution

To solve this problem, we'll apply the straightforward approach of summing up the lengths of all four sides of the trapezoid to determine its perimeter:

  • Step 1: Identify the side lengths: the top base is 66, the bottom base is 14.5214.52, the left side is 4.14.1, and the right side is 9.879.87.
  • Step 2: Apply the perimeter formula for the trapezoid: P=a+b+c+d P = a + b + c + d , where a=6a = 6, b=14.52b = 14.52, c=4.1c = 4.1, and d=9.87d = 9.87.
  • Step 3: Add the side lengths: P=6+14.52+4.1+9.87 P = 6 + 14.52 + 4.1 + 9.87 .

Now, performing the calculation:

P=6+14.52+4.1+9.87=34.49 P = 6 + 14.52 + 4.1 + 9.87 = 34.49

Therefore, the perimeter of the trapezoid is 34.49 34.49 .

Answer

34.49

Exercise #10

Calculate the perimeter of the trapezoid below:

12.2812.2812.2866617.517.517.55.15.15.1

Step-by-Step Solution

To solve this problem, we'll use the perimeter formula for a trapezoid, which is straightforward since all side lengths are provided:

  • Step 1: Identify the side lengths:
    Top base (aa): 12.2812.28 units
    Bottom base (bb): 17.517.5 units
    Left non-parallel side (cc): 5.15.1 units
    Right non-parallel side (dd): 66 units
  • Step 2: Apply the formula for the perimeter, which states:
    P=a+b+c+d P = a + b + c + d
  • Step 3: Substitute the known values into the formula:
    P=12.28+17.5+5.1+6 P = 12.28 + 17.5 + 5.1 + 6
  • Step 4: Perform the addition:

Calculating the sum:

12.28+17.5=29.78 12.28 + 17.5 = 29.78

29.78+5.1=34.88 29.78 + 5.1 = 34.88

34.88+6=40.88 34.88 + 6 = 40.88

Hence, the perimeter of the trapezoid is 40.8840.88 units.

Answer

40.88

Exercise #11

What is the perimeter of the trapezoid in the figure?

7.57.57.54441.51.51.5333

Video Solution

Answer

16

Exercise #12

Look at the trapezoid in the figure.

Calculate its perimeter.

2.52.52.510.410.410.45.35.35.3666

Video Solution

Answer

24.2

Exercise #13

Given the trapezoid:

444999666131313

What is its perimeter?

Video Solution

Answer

32

Exercise #14

AB = 5

CD = 7

AC = 4

BD = 4

Calculate the perimeter of the rectangle.

555444777444AAABBBDDDCCC

Video Solution

Answer

20

Exercise #15

AB = 10.5

CD = 13

AC = 7.5

BD = 7.5

Calculate the perimeter of the rectangle ABCD.

10.510.510.57.57.57.51313137.57.57.5AAABBBDDDCCC

Video Solution

Answer

38.5

Exercise #16

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

777101010777121212AAABBBCCCDDD

Video Solution

Answer

36

Exercise #17

The drawing shows an isosceles trapezoid.

What is its perimeter?

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Video Solution

Answer

20

Exercise #18

Look at the trapezoid in the figure.

Express the perimeter of the trapezoid using the given variables.

5X5X5X3X3X3XZZZ3Y3Y3Y

Video Solution

Answer

8X+3Y+Z

Exercise #19

Below is an isosceles trapezoid:

101010121212666 What is its perimeter?

Video Solution

Answer

34

Exercise #20

The trapezoid below is isosceles.

AB = 20

CD = 25

BD = 8

Calculate its perimeter.

202020888252525AAABBBDDDCCC

Video Solution

Answer

61