Perimeter of a Trapezoid - Examples, Exercises and Solutions

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!

The problem requires calculating the perimeter of the trapezoid by summing the lengths of its sides. Based on the given trapezoid diagram, the side lengths are clearly marked as follows:

• First side: $4$
• Second side: $9$
• Third side: $6$
• Fourth side: $13$

According to the formula for the perimeter of a trapezoid:

$P = a + b + c + d$

Substituting the respective values:

$P = 4 + 9 + 6 + 13$

Calculating the sum, we find:

$P = 32$

Thus, the perimeter of the trapezoid is $32$.

To find the perimeter we will add all the sides:

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

To find the perimeter of the trapezoid, we will sum the lengths of all its sides. The given side lengths are:

• Base 1: $7.5$
• Base 2: $1.5$
• Leg 1: $3$
• Leg 2: $4$

Using the formula for the perimeter $P$ of the trapezoid, we have:

$P = a + b + c + d$

Substituting in the given values:

$P = 7.5 + 1.5 + 3 + 4$

Performing the addition:

$P = 7.5 + 1.5 = 9$

$P = 9 + 3 = 12$

$P = 12 + 4 = 16$

Therefore, the perimeter of the trapezoid is $16$.

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

• Step 1: Identify all given side lengths of the trapezoid.
• Step 2: Apply the formula for the perimeter of the trapezoid.
• Step 3: Sum up the lengths to find the perimeter.

Now, let's work through each step:
Step 1: The problem gives us the lengths of the trapezoid's sides:
- $AB = 2.5$
- $BC = 10.4$
- $CD = 5.3$
- $DA = 6$

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

$P = AB + BC + CD + DA$

Step 3: Plugging in the given values, we calculate:

$P = 2.5 + 10.4 + 5.3 + 6$

Calculating further, we have:

$P = 24.2$

Therefore, the perimeter of the trapezoid is $24.2$.

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

• Step 1: Identify the given measurements for the sides.

• Step 2: Use the perimeter formula for a trapezoid, which is summing all sides.

• Step 3: Add the values to get the perimeter.

Now, let's work through each step:

Step 1: The problem gives us four sides to consider. These sides are: $AB = 5$, $CD = 7$, $AC = 4$, and $BD = 4$.

Step 2: The perimeter of a trapezoid or any quadrilateral is simply the sum of all four sides. Hence, we need to add $AB$, $CD$, $AC$, and $BD$.

Step 3: Adding the values, we calculate the perimeter:$AB + CD + AC + BD = 5 + 7 + 4 + 4 = 20$.

Therefore, the perimeter of the given shape is $20$.

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

• Step 1: Gather the given side lengths of quadrilateral ABCD.

• Step 2: Since it's necessary to understand summation, add all lengths.

• Step 3: Conclude from sum.

Now, let's work through each step:

Step 1: The problem provides:
$\begin{aligned} AB &= 10.5, \\ CD &= 13, \\ AC &= 7.5, \\ BD &= 7.5. \end{aligned}$

Step 2: Add them together:
$\begin{aligned} \text{Perimeter} &= AB + CD + AC + BD \\ &= 10.5 + 13 + 7.5 + 7.5. \end{aligned}$

Step 3: Calculate: $\begin{aligned} \text{Perimeter} &= 10.5 + 13 + 7.5 + 7.5 = 38.5. \end{aligned}$

Therefore, the solution is that the perimeter of quadrilateral ABCD is $38.5$ .

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

Therefore, the perimeter of the trapezoid is $36$.

This matches the correct answer choice from the provided options.

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 $9$, $5$, $12$, and $4$.
Step 2: The formula for the perimeter $P$ of a trapezoid is:
$P = \text{side}_1 + \text{side}_2 + \text{side}_3 + \text{side}_4$
Step 3: Plugging in the values, we compute:
$P = 9 + 5 + 12 + 4$
Step 4: Calculating the sum:
$P = 30$

Therefore, the perimeter of the trapezoid is $30$.

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

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

$P = a + b + c + d$

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

$P = 16 + 1 + 15 + 16$

$P = 48$

Therefore, the perimeter of the trapezoid is $48$.

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

Therefore, the perimeter of the trapezoid is $36$.

To calculate the perimeter of the isosceles trapezoid, we follow these steps:

• Identify the lengths of all the sides.
• Sum these lengths to find the perimeter.

Now, let's apply these steps:
Step 1: The given lengths of the trapezoid are:
- Base 1 = $10$,
- Base 2 = $12$,
- Each leg = $6$.

Step 2: Using the perimeter formula $P = a + b + c + d$, we get:
$P = 10 + 12 + 6 + 6$.

Step 3: Adding these values, we find:
$P = 34$.

Therefore, the perimeter of the isosceles trapezoid is $34$.

To find the perimeter of the isosceles trapezoid, consider the following steps:

• Step 1: Identify the given side lengths: The top base of the trapezoid is $3$, each of the slanted sides is $5$, and the bottom base is $7$.
• Step 2: Apply the perimeter formula: The perimeter $P$ is the sum of all side lengths: $P = 3 + 5 + 5 + 7$.
• Step 3: Perform the calculation: Add the side lengths together:
  $3 + 5 + 5 + 7 = 20$

Therefore, the perimeter of the isosceles trapezoid is $20$.

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

Multiply the short base by 1.5:

$5\times1.5=7.5$

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

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

To solve this problem, we'll express the perimeter of the trapezoid by summing up its side lengths:

• Step 1: Identify the given side lengths.

• Step 2: Apply the perimeter formula for the trapezoid.

• Step 3: Simplify the resulting expression.

Let's work through these steps:

Step 1: The trapezoid has the following side lengths:
- Top base: $5X$
- Left side: $3X$
- Bottom base: $Z$
- Right side: $3Y$

Step 2: Apply the perimeter formula:
The perimeter $P$ is given by the sum of all sides:
\begin{equation} $P = 5X + 3X + Z + 3Y$

Step 3: Simplify the expression:
Combine like terms:
$P = (5X + 3X) + Z + 3Y = 8X + 3Y + Z$

Therefore, the perimeter of the trapezoid is expressed as $8X + 3Y + Z$.