### Area of a Parallelogram #### Lesson Objective

In this lesson, we will learn about the area of a parallelogram. In this lesson, we will:

• Learn about the formula for the area of a parallelogram.
• See an example on using the formula to find a parallelogram's area.
• See another example on using the formula to calculate the height of a parallelogram.

The study tips and math video below will explain more. ### Study Tips #### Tip #1

A parallelogram has two pairs of parallel sides and its opposite sides are equal in length. These properties are shown on the right.

Now, if the parallelogram has the base b and the height h, the area, A, of the parallelogram will be:

A = bh

The math video below will give more explanation on this. Also, we will see some examples on how to use this formula.  ### Math Video #### Lesson Video #### Math Video Transcript

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In this lesson, we will learn about the area of a parallelogram.

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Consider this parallelogram with the base B and the height H.

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Now, to find the area of this parallelogram, A, let's observe this parallelogram carefully.

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If we cut out this portion and place it here. Observe that, we now have a rectangle.

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Therefore, we can say that the area of this parallelogram is that same as, the area of this rectangle.

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In the previous lesson, we learned that the area of a rectangle can be found by multiplying its length and width together.

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Similarly, we can find this area, by multiplying the base, and height together. Hence, we have B multiply H which is the same as BH.

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Let's change this back to a parallelogram. Now, the area of this parallelogram, A, equals to BH.

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Note that, it is very important to include the unit. Since this is the formula for area, its unit will be in the form of square unit.

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We will see more explanations on this, in the upcoming example.

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Now, let's see some examples on using this formula.

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Find the area of this parallelogram when its base is 5cm, and its height is 3cm.

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To solve this, we start with the formula for the area of a parallelogram, A equals to BH.

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Since the base is given as 5cm, we can substitute b with 5.

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Similarly, since the height is given as 3cm, we can substitute h with 3.

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Next, we can simplify by multiplying 5 with 3. This gives 15.

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Note that, this number has no meaning unless we include the unit for it.

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Since the units are given in centimeter, the unit for the area will be in square centimeter.

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Hence, the area of this parallelogram is 15 square centimeter.

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Next example, given that the area of this parallelogram is 20 square feet, and its base is 4ft. Find its height.

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Again, we start with the formula for the area of a parallelogram, A equals to BH.

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Now, since the area, and the base are given, we can find the height by solving this equation for H. Here’s how.

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Since the area is given as 20 square feet, we can substitute A with 20.

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Similarly, since the base is given as 4cm, we can substitute b with 4.

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Now we have, 4H equals to 20.

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Let's rewrite this equation so that it will look neater.

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To find h, we need to remove 4. We can do so by dividing both sides of the equation with 4.

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By doing so, we have, H equals to 20 over 4.

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20 divides by 4, gives 5.

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Now, this number is meaningless unless we include the unit for it.

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Since the base is in feet, the height of the parallelogram will be in feet.

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Therefore, the height of this parallelogram is 5 ft.

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That is all for this lesson. Try out the practice question to further your understanding.

### Practice Questions & More #### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the area of a parallelogram or pick your choice of question below.

• Question 1 on finding the area of a parallelogram
• Question 2 on finding the height of a parallelogram #### Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there. 