Given the parallelogram of the figure What is your area? 9 9 9 5 5 5 A A A B B B C C C D D D E E E

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Area of Parallelogram Practice Problems and Solutions

Master parallelogram area calculations with step-by-step practice problems. Learn formulas, work through examples, and build confidence in geometry.

📚What You'll Master in This Practice Session

Apply the area formula A = base × height to solve parallelogram problems
Calculate missing dimensions when given area and one measurement
Identify correct base-height pairs in parallelogram diagrams
Solve complex problems involving parallelograms with external heights
Work with ratios and proportions in parallelogram area calculations
Distinguish between different types of parallelograms (rectangle, rhombus, square)

Understanding Area of a Parallelogram

Complete explanation with examples

How is the area of a parallelogram calculated?

We can calculate the area of a parallelogram by multiplying one of its sides by its relative height.

To understand it better, we can use the following figure and the accompanying formula:

$A=DC\times H1=BC\times H2$

It can be seen that: $H1$ and $H2$ are the two heights corresponding to the bases $DC$ and $BC$ respectively.

Area of a Parallelogram

Detailed explanation

Practice Area of a Parallelogram

Test your knowledge with 23 quizzes

AB = 5 cm

The height of the rectangle is 2 cm.

Calculate the area of the parallelogram.

Examples with solutions for Area of a Parallelogram

Step-by-step solutions included

Exercise #1

Calculate the area of the following parallelogram:

Step-by-Step Solution

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 $60 \, \text{cm}^2$ .

Answer:

60 cm²

Video Solution

Exercise #2

Calculate the area of the following parallelogram:

Step-by-Step Solution

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

Answer:

30 cm²

Video Solution

Exercise #3

ABCD is a parallelogram.

AH is the height.

DC = 6
AH = 3

What is the area of the parallelogram?

Step-by-Step Solution

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 $18 \, \text{cm}^2$ .

Answer:

18 cm²

Video Solution

Exercise #4

ABCD is a parallelogram.

AH is its height.

Given in cm:

AB = 7

AH = 2

Calculate the area of the parallelogram.

Step-by-Step Solution

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 $\textbf{14 cm}^2$ .

Answer:

14 cm².

Video Solution

Exercise #5

Given the parallelogram of the figure

What is your area?

Step-by-Step Solution

To find the area of the parallelogram, we will use the formula:

A = \text{base} \times \text{height}

From the problem, we identify the base as $7 \, \text{cm}$ and the height as $4 \, \text{cm}$ . Substituting these values into the formula, we get:

A = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2

Therefore, the area of the parallelogram is $28 \, \text{cm}^2$ .

Answer:

$28\operatorname{cm}^2$

Video Solution

Frequently Asked Questions

Everything you need to know about Area of a Parallelogram

What is the formula for finding the area of a parallelogram?

The area of a parallelogram is calculated using the formula A = base × height, where the height must be perpendicular to the chosen base. You can use any side as the base, but you must use its corresponding perpendicular height.

How do I identify the height of a parallelogram in a diagram?

The height is always the perpendicular distance between two parallel sides. Look for: 1) A line segment drawn at a 90° angle to the base, 2) Dashed lines indicating perpendicular measurements, 3) Right angle symbols (small squares) showing where height meets the base.

Can I use any side as the base when calculating parallelogram area?

Yes, you can use any side as the base. However, you must use the height that corresponds to that specific base - the perpendicular distance to the opposite parallel side. Different base-height pairs should give the same area result.

What's the difference between a parallelogram's side length and its height?

A parallelogram's side length is the actual length of one of its four sides, while the height is the perpendicular distance between parallel sides. The height is usually shorter than the slanted sides and forms a 90° angle with the base.

How do I solve parallelogram area problems with missing measurements?

Use the area formula A = base × height and substitute known values. For missing dimensions: 1) Rearrange the formula (height = area ÷ base, or base = area ÷ height), 2) Use properties like opposite sides being equal, 3) Apply given ratios or relationships between measurements.

What are common mistakes when calculating parallelogram area?

Common errors include: • Using a side length instead of the perpendicular height • Confusing slant height with perpendicular height • Not checking that both base-height calculations give the same area • Forgetting that opposite sides of parallelograms are equal

How is parallelogram area different from rectangle or square area?

While rectangles and squares use length × width, parallelograms require base × perpendicular height because their sides are slanted. Rectangles and squares are special parallelograms where all angles are 90°, making side length equal to height.

What real-world applications use parallelogram area calculations?

Parallelogram area is used in: architecture for calculating sloped roof areas, engineering for determining material needs for angled structures, graphic design for layout planning, and construction for estimating flooring or tiling for non-rectangular spaces.

Continue Your Math Journey

Master Area of a Parallelogram first, then advance to these related topics that build on your fraction skills

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Area of Parallelogram Practice Problems and Solutions

Understanding Area of a Parallelogram

How is the area of a parallelogram calculated?

Practice Area of a Parallelogram

Examples with solutions for Area of a Parallelogram

Frequently Asked Questions

What is the formula for finding the area of a parallelogram?

How do I identify the height of a parallelogram in a diagram?

Can I use any side as the base when calculating parallelogram area?

What's the difference between a parallelogram's side length and its height?

How do I solve parallelogram area problems with missing measurements?

What are common mistakes when calculating parallelogram area?

How is parallelogram area different from rectangle or square area?

What real-world applications use parallelogram area calculations?

More Area of a Parallelogram Questions

Area of a Parallelogram

Continue Your Math Journey

Topics Learned in Later Sections

Practice by Question Type