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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Parallelogram Practice Problems & Exercises with Solutions

Master parallelogram properties, angle calculations, and verification methods with step-by-step practice problems. Perfect for geometry students learning quadrilaterals.

📚What You'll Master in This Parallelogram Practice

Identify and apply properties of parallelograms including opposite sides and angles
Calculate unknown angles using alternate interior and corresponding angle relationships
Verify if quadrilaterals are parallelograms using four different proof methods
Solve for missing side lengths and diagonal measurements in parallelograms
Apply parallelogram properties to find perimeter and area calculations
Master diagonal intersection properties and bisection theorems

Understanding Parallelogram

Complete explanation with examples

Parallelogram

Parallelogram is a four-sided polygon (quadrilateral) where opposite sides are parallel and equal in length. A key feature of parallelograms is that they have two sets of parallel lines, which gives them their name. Examples of parallelograms include squares, rectangles, and rhombuses, which are all specific types of parallelograms with additional unique properties.

Characteristics of the Parallelogram

Sides opposite in a quadrilateral: are sides that do not have a common meeting point.
Adjacent sides in a quadrilateral: are sides that have a common meeting point.
Adjacent angles: are 2 angles that have a common vertex and side.
Opposite angles in the quadrilateral are angles that do not have common sides.
Diagonal: is a section that connects 2 non-adjacent vertices (and is not a side)

If the data is:

$AB ǁ CD$
$AD ǁ BC$

Then: $ABCD$ is a parallelogram

Parallelogram

Detailed explanation

Practice Parallelogram

Test your knowledge with 44 quizzes

AB = 5 cm

The height of the rectangle is 2 cm.

Calculate the area of the parallelogram.

Examples with solutions for 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 Parallelogram

What are the 4 main properties of a parallelogram?

The four main properties are: 1) Opposite sides are parallel and equal, 2) Opposite angles are equal, 3) Diagonals bisect each other, and 4) Adjacent angles are supplementary (add up to 180°).

How do you prove a quadrilateral is a parallelogram?

You can prove a quadrilateral is a parallelogram using any of these methods: • Show both pairs of opposite sides are parallel • Prove both pairs of opposite sides are equal • Demonstrate both pairs of opposite angles are equal • Show diagonals bisect each other • Prove one pair of opposite sides is both parallel and equal

What is the difference between corresponding angles and alternate interior angles in parallelograms?

Corresponding angles are in the same position at each intersection when a transversal crosses parallel lines. Alternate interior angles are on opposite sides of the transversal and inside the parallel lines, forming a 'Z' pattern. Both are equal when lines are parallel.

How do you find missing angles in a parallelogram?

Use these steps: 1) Remember opposite angles are equal, 2) Adjacent angles are supplementary (add to 180°), 3) Apply alternate interior angle theorem for parallel sides, 4) Use the fact that all four angles sum to 360°.

What happens when diagonals of a parallelogram intersect?

When diagonals of a parallelogram intersect, they bisect each other at the point of intersection. This means each diagonal is divided into two equal segments, creating four congruent triangles within the parallelogram.

Can a parallelogram have right angles?

Yes, a parallelogram can have right angles. When all angles are 90°, it becomes a rectangle. A rectangle is a special type of parallelogram with additional properties like equal diagonals and four right angles.

How do you calculate the perimeter of a parallelogram?

The perimeter formula is P = 2(a + b), where 'a' and 'b' are the lengths of adjacent sides. Since opposite sides are equal in a parallelogram, you only need to measure two adjacent sides and double their sum.

What are real-world examples of parallelograms?

Common real-world parallelograms include: railway tracks forming parallelograms at intersections, rectangular picture frames, rhombus-shaped tiles, parallelogram-shaped building windows, and the quadrilateral formed by opposite pages in an open book.

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Applying the formula Calculate The Missing Side based on the formula Calculating in two ways Finding Area based off Perimeter and Vice Versa Using additional geometric shapes Using congruence and similarity Using external height Using Pythagoras' theorem Using ratios for calculation Using variables Verifying whether or not the formula is applicable Calculating angle size in a parallelogram Calculating the length of a side in a parallelogram In order for the quadrilateral to be a parallelogram what should the value of the unknown be ? Is this a parallelogram? True / false Using the properties of the perimeter of the parallelogram

Parallelogram Practice Problems & Exercises with Solutions

Understanding Parallelogram

Parallelogram

Parallelogram

Practice Parallelogram

Examples with solutions for Parallelogram

Frequently Asked Questions

What are the 4 main properties of a parallelogram?

How do you prove a quadrilateral is a parallelogram?

What is the difference between corresponding angles and alternate interior angles in parallelograms?

How do you find missing angles in a parallelogram?

What happens when diagonals of a parallelogram intersect?

Can a parallelogram have right angles?

How do you calculate the perimeter of a parallelogram?

What are real-world examples of parallelograms?

More Parallelogram Questions

Area of a Parallelogram

Parallelogram

Characteristics and Proofs of a Parallelogram

Practice by Question Type

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