Parallelogram - Examples, Exercises and Solutions

In this particular problem, despite being given certain measurements, the diagram lacks sufficient clarity to identify which corresponds definitively as the base and which as the perpendicular height of the parallelogram. This insufficiency means that without further context or labeling to avoid assumptions that may lead to error, it is not feasible to calculate the area confidently using the standard formula.

Thus, the answer to the problem is that it is not possible to calculate the area with the provided data.

To solve this problem, let's apply the formula for the area of a parallelogram:

The formula for the area of a parallelogram is $\text{Area} = \text{base} \times \text{height}$.

Here, the base of the parallelogram is 6 cm, and the height is 4.5 cm.

Substituting these values into the formula gives:

$\text{Area} = 6 \times 4.5$

Performing the multiplication:

$\text{Area} = 27$ square centimeters.

Therefore, the area of the parallelogram is $27 \, \text{cm}^2$.

Referring to the given multiple-choice answers, the correct choice is:

Choice 3: $27$.

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

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

Now, let's work through each step:
Step 1: The problem provides us with a base ($b$) of 7 units and a height ($h$) of 5 units, perpendicular to this base.
Step 2: We'll apply the formula for the area of a parallelogram, which is $\text{Area} = b \times h$.
Step 3: Substituting the given values, $\text{Area} = 7 \times 5 = 35$.

Therefore, the area of the parallelogram is $35$ square units.

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

• Step 1: Identify the base and height from the information provided.
• Step 2: Apply the formula for the area of a parallelogram.
• Step 3: Calculate the area by multiplying the base and height.

Now, let's work through each step:
Step 1: The base of the parallelogram is given as $8$ units, and the height is given as $5$ units.
Step 2: We use the formula for the area of a parallelogram: $\text{Area} = \text{base} \times \text{height}$.
Step 3: Plugging in the given values, we calculate the area as follows:
$\text{Area} = 8 \times 5 = 40$.

Therefore, the area of the parallelogram is $40$ square units, which corresponds to choice 2.

To solve this problem, we must calculate the area of the given parallelogram using the formula:

$\text{Area} = \text{base} \times \text{height}$

Assuming the figure (as described) provides a base of $9$ units and a height of $4$ units, we substitute these values into the formula:

$\text{Area} = 9 \times 4 = 36 \text{ square units}$

The necessary calculations have been carried out using the correct dimensions, ensuring dimensional consistency and precise arithmetical methods. Therefore, the calculated area of the parallelogram is $36$.

Given the multiple-choice options, the correct choice is the one specifying the area as $36$, confirming the answer provided in choice 3.

From the given constraints, it is impossible to confidently compute the area of the parallelogram because of insufficient and unclear relationships between provided figures and the calculations they must produce. Clarity on which numbers correspond to the height and base—as or any definitional angles—is absent.

The correct answer, aligning with acknowledged drawing limitations, is: It is not possible to calculate.

To calculate the area of the parallelogram, we will simply apply the formula for the area of a parallelogram:

• Identify the base: The length of the base is $10 \, \text{cm}$.
• Identify the height: The perpendicular height is given as $6 \, \text{cm}$.

Apply the formula: $\text{Area} = \text{base} \times \text{height}$.

Substitute the known values: $\text{Area} = 10 \, \text{cm} \times 6 \, \text{cm}$.

Calculate the result: $\text{Area} = 60 \, \text{cm}^2$.

Therefore, the area of the parallelogram is $60 \, \text{cm}^2$.

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

• Step 1: Identify the given base and height.
• Step 2: Apply the formula for the area of a parallelogram.
• Step 3: Calculate the area using the provided dimensions.

Now, let's work through each step:
Step 1: The base $b$ is equal to the length $AB$, which is $\text{15 cm}$. The height $h$ corresponding to this base is $\text{6 cm}$.
Step 2: We'll use the formula for the area of a parallelogram:
$\text{Area} = b \times h$.
Step 3: Plugging in our values, we have:
$\text{Area} = 15 \times 6 = 90 \, \text{cm}^2$.

Therefore, the solution to the problem is $\text{Area} = 90 \, \text{cm}^2$, which matches choice .

To solve the exercise, we need to remember the formula for the area of a parallelogram:

Side * Height perpendicular to the side

In the diagram, although it's not presented in the way we're familiar with, we are given the two essential pieces of information:

Side = 6

Height = 5

Let's now substitute these values into the formula and calculate to get the answer:

6 * 5 = 30

To solve this problem, we'll apply the formula for the area of a parallelogram:

• Step 1: Identify the base and the height from the given information.
• Step 2: Use the formula for the area of a parallelogram: $A = \text{base} \times \text{height}$.
• Step 3: Calculate the area using the given values.

Let's proceed with the solution:
Step 1: The given base $AB$ is 10 cm, and the height is 5 cm.
Step 2: The formula for the area of a parallelogram is $A = \text{base} \times \text{height}$.
Step 3: Substituting the provided values, we get:
$A = 10 \, \text{cm} \times 5 \, \text{cm}$
$A = 50 \, \text{cm}^2$

Therefore, the area of the parallelogram is $50 \, \text{cm}^2$.

To calculate the area of the parallelogram, we'll use the standard area formula for a parallelogram:

$\text{Area} = \text{base} \times \text{height}$

From the problem, the base $AB = 32 \, \text{cm}$ and the height is $15 \, \text{cm}$.

Substituting these values into the formula gives:

$\text{Area} = 32 \times 15$

Perform the multiplication:

$32 \times 15 = 480$

Thus, the area of the parallelogram is $\text{480 cm}^2$.

The correct answer is choice 4: 480.

To solve this problem, let's apply the formula for the area of a parallelogram:

• The given base $DC$ is 6 cm.
• The perpendicular height $AH$ from point $A$ to base $DC$ is 3 cm.

The formula for the area of a parallelogram is:

$\text{Area} = \text{base} \times \text{height}$

Substituting the given values, we have:

$\text{Area} = 6 \times 3$

Thus, the area of parallelogram $ABCD$ is:

$\text{Area} = 18 \, \text{cm}^2$

Therefore, the solution to the problem is $18 \, \text{cm}^2$.

To find the area of the parallelogram, we will follow these steps:

• Identify the base and the corresponding height.
• Use the formula for the area of a parallelogram.
• Perform the calculation to find the area.

Let's execute these steps:

Step 1: Identify the given measurements. The base $AB = 5 \, \text{cm}$, and the height corresponding to it is $2 \, \text{cm}$.

Step 2: Apply the formula for the area of a parallelogram, which is $A = b \times h$.

Step 3: Substitute the known values into the formula:
$A = 5 \, \text{cm} \times 2 \, \text{cm} = 10 \, \text{cm}^2$

Therefore, the area of the parallelogram is $10 \, \text{cm}^2$.

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

• Step 1: Identify the base and height.
  Here, the base $AB$ is $7 \, \text{cm}$ and the perpendicular height $AH$ is $2 \, \text{cm}$.
• Step 2: Use the area formula for a parallelogram:
  $\text{Area} = \text{base} \times \text{height}$
• Step 3: Substitute the given values into the formula:
  $\text{Area} = 7 \times 2 = 14 \, \text{cm}^2$

Therefore, the area of the parallelogram is $\textbf{14 cm}^2$.

To calculate the area of the parallelogram, we'll use the formula for the area, which is the product of the base and the height.

• Identify the base and height from the information given: The base $AB$ is 25 cm and the height is 13 cm.
• Apply the formula for the area: $\text{Area} = \text{Base} \times \text{Height}$.
• Substitute the given values into the formula: $\text{Area} = 25 \times 13$.
• Perform the multiplication: $\text{Area} = 325$ square centimeters.

Therefore, the area of the parallelogram is $325 \, \text{cm}^2$.

This corresponds to choice 1: 325.