Perimeter of a Parallelogram - Examples, Exercises and Solutions

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

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

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

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

To solve this problem, let's follow these steps:

• Step 1: Identify the lengths of the adjacent sides of the parallelogram.
• Step 2: Use the formula for the perimeter of a parallelogram, $P = 2(a + b)$.
• Step 3: Plug in the known values and calculate the perimeter.

Now, let's work through each step:

Step 1: From the diagram, we have two adjacent sides of the parallelogram: $a = 8$ units and $b = 3$ units.

Step 2: The formula for the perimeter of a parallelogram is given by $P = 2(a + b)$.

Step 3: Substitute the values for $a$ and $b$ into the formula:

$P = 2(8 + 3) = 2 \times 11 = 22$.

Therefore, the perimeter of the parallelogram is $22$.

To solve the problem of calculating the perimeter of the parallelogram, follow these steps:

• Identify the given side lengths: $AB = 5$ and $AC = 4$.
• Acknowledge that in a parallelogram, opposite sides are equal, so $AB = CD = 5$ and $AC = BD = 4$.
• Apply the perimeter formula for a parallelogram: $P = 2 \times ( \text{Base} + \text{Side} )$.

Plug the known side lengths into the formula:
$P = 2 \times (AB + AC) = 2 \times (5 + 4) = 2 \times 9 = 18$

Thus, the perimeter of the parallelogram is $18$.

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

Therefore it is possible to argue that:

$AC=BD=7$

$AB=CD=10$

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

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

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

• Step 1: Identify the given side lengths of the parallelogram.
• Step 2: Apply the perimeter formula for a parallelogram.
• Step 3: Perform the calculation with the identified side lengths.

Now, let's work through each step:
Step 1: The problem gives us the side lengths of the parallelogram as $AB = 5$ and $BC = 2$. Since opposite sides are equal in a parallelogram, we have $AB = CD = 5$ and $BC = DA = 2$.
Step 2: We'll use the formula for the perimeter of a parallelogram: $P = 2(a + b)$.
Step 3: Substituting the values, we have:

Therefore, the perimeter of the parallelogram is $\boxed{14}$.

The correct multiple-choice answer is 14, which corresponds to choice number 2.

To determine the perimeter of the parallelogram, we need first to identify the lengths of the sides:

• From the problem, one side ($a$) is $9$ units, and an adjacent side ($b$) is $3$ units.

Using the formula for the perimeter of a parallelogram, $P = 2(a + b)$, we can substitute the known values:

• $a = 9$
• $b = 3$

Substituting these values into the formula gives us:

$P = 2(9 + 3)$

$P = 2 \times 12$

$P = 24$

Therefore, the perimeter of the parallelogram is $24$.

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

• Step 1: Identify the given side lengths
• Step 2: Use the perimeter formula for a parallelogram
• Step 3: Perform the calculation to find the perimeter

Now, let's work through each step:
Step 1: The problem tells us that the lengths of two adjacent sides of the parallelogram are 15 and 10.
Step 2: We'll use the formula for the perimeter of a parallelogram, which is $P = 2(a + b)$, where $a$ and $b$ are the two sides.
Step 3: Plugging in the values, we have $P = 2(15 + 10) = 2 \times 25 = 50$.

Therefore, the perimeter of the parallelogram is $50$.

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

• Step 1: Identify the lengths of the sides of the parallelogram.
• Step 2: Apply the perimeter formula for a parallelogram.
• Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: The given information tells us that one side $AB$ is $10$, and the adjacent side $AC$ is $8$.
Step 2: The perimeter $P$ of a parallelogram is given by the formula $P = 2 \times (\text{base} + \text{side})$.
Step 3: We substitute the lengths we have: $P = 2 \times (10 + 8) = 2 \times 18 = 36$

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

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:

In our shape, let’s define:

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

Plugging these values into our formula, we get:

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

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

• Step 1: Identify the given side lengths of the parallelogram.
• Step 2: Use the perimeter formula for a parallelogram, $P = 2(a + b)$.
• Step 3: Perform the calculation to find the perimeter.

Let's proceed with the solution:

Step 1: The problem provides the side lengths of the parallelogram as $AB = 20$ units and $AD = 15$ units.

Step 2: Use the formula for the perimeter of a parallelogram, $P = 2(a + b)$, where $a = 20$ and $b = 15$.

Step 3: Plug the side lengths into the formula:

Calculating further, we get:

Therefore, the perimeter of the parallelogram is $70$.

To find the perimeter of the parallelogram, we apply the formula $P = 2(a + b)$, where $a$ and $b$ are the lengths of adjacent sides.

Step-by-step:

• Step 1: Identify the side lengths. From the given problem, $a = 17$ and $b = 13$.
• Step 2: Use the perimeter formula $P = 2(a + b)$.
• Step 3: Substitute the given values into the formula.

Calculation:

$P = 2(17 + 13)$

$P = 2 \times 30$

$P = 60$

Therefore, the perimeter of the parallelogram is $60$.

To determine the perimeter of the parallelogram, follow these steps:

• Step 1: Note the given side lengths of the parallelogram. Side $AB = 6.5$ and side $AD = 4.5$.
• Step 2: Apply the perimeter formula for a parallelogram: $P = 2(a + b)$, where $a$ and $b$ are the lengths of two adjacent sides.
• Step 3: Substitute the given lengths into the formula:

$P = 2 \times (6.5 + 4.5)$

Step 4: Perform the addition inside the parentheses: $6.5 + 4.5 = 11$

Step 5: Multiply the sum by 2 to find the perimeter: $P = 2 \times 11 = 22$

Therefore, the solution to the problem is that the perimeter of the parallelogram is $P = 22$.

Upon reviewing the choices, the correct answer is choice 4: 22.

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

• Step 1: Identify the side lengths of the parallelogram.
• Step 2: Apply the perimeter formula for a parallelogram.
• Step 3: Calculate the perimeter using the given side lengths.

Now, let's work through each step:
Step 1: The side lengths given are $a = 14$ and $b = 11$.
Step 2: Apply the formula for the perimeter of a parallelogram, which is $P = 2(a + b)$.
Step 3: Substitute the values into the formula: $P = 2(14 + 11) = 2 \times 25 = 50$.

Therefore, the solution to the problem is $P = 50$.

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

• Step 1: Identify the given side lengths of the parallelogram.
• Step 2: Apply the formula for the perimeter of a parallelogram.
• Step 3: Calculate the perimeter using the identified side lengths.

Now, let's work through each step:
Step 1: The problem states that the lengths of sides AB and BC in the parallelogram are 11 and 7 units, respectively.
Step 2: The formula for the perimeter $P$ of a parallelogram is $P = 2 \times (\text{side 1} + \text{side 2})$.
Step 3: Substituting the given lengths into the formula, we have:
$P = 2 \times (11 + 7) = 2 \times 18 = 36$.

Therefore, the perimeter of the parallelogram is $\mathbf{36}$ units.

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

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

Proceeding with the calculation:

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

Therefore, the perimeter of the parallelogram is 12 units.