Area of a Parallelogram - Examples, Exercises and Solutions

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×H1=BC×H2 A=DC\times H1=BC\times H2

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

Area of a Parallelogram

A5 - Parallelogram area formula

Detailed explanation

Practice Area of a Parallelogram

Test your knowledge with 23 quizzes

AB = 5 cm

The height of the rectangle is 2 cm.

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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:

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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 10cm10 \, \text{cm}.
  • Identify the height: The perpendicular height is given as 6cm6 \, \text{cm}.

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

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

Calculate the result: Area=60cm2 \text{Area} = 60 \, \text{cm}^2 .

Therefore, the area of the parallelogram is 60cm2 60 \, \text{cm}^2 .

Answer:

60 cm²

Video Solution
Exercise #2

Calculate the area of the following parallelogram:

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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?

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Step-by-Step Solution

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

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

The formula for the area of a parallelogram is:

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

Substituting the given values, we have:

Area=6×3 \text{Area} = 6 \times 3

Thus, the area of parallelogram ABCDABCD is:

Area=18cm2 \text{Area} = 18 \, \text{cm}^2

Therefore, the solution to the problem is 18cm218 \, \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.

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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 AB is 7cm 7 \, \text{cm} and the perpendicular height AH AH is 2cm 2 \, \text{cm} .
  • Step 2: Use the area formula for a parallelogram:
    Area=base×height \text{Area} = \text{base} \times \text{height}
  • Step 3: Substitute the given values into the formula:
    Area=7×2=14cm2 \text{Area} = 7 \times 2 = 14 \, \text{cm}^2

Therefore, the area of the parallelogram is 14 cm2 \textbf{14 cm}^2 .

Answer:

14 cm².

Video Solution
Exercise #5

Given the parallelogram of the figure

What is your area?

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Step-by-Step Solution

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

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

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

A=7cm×4cm=28cm2 A = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2

Therefore, the area of the parallelogram is 28cm2 28 \, \text{cm}^2 .

Answer:

28cm2 28\operatorname{cm}^2

Video Solution

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