### Area of a Parallelogram

#### Lesson Objective

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

#### About This Lesson

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:

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

### Math Video

#### Math Video Transcript

00:00:03.170

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

00:00:08.120

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

00:00:14.190

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

00:00:22.060

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

00:00:30.150

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

00:00:38.050

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

00:00:46.240

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.

00:00:59.180

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

00:01:09.210

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.

00:01:19.160

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

00:01:25.020

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

00:01:29.220

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

00:01:37.110

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

00:01:44.240

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

00:01:51.010

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

00:01:57.240

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

00:02:05.020

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

00:02:10.070

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

00:02:16.070

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

00:02:22.240

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

00:02:32.130

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

00:02:39.190

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

00:02:48.210

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

00:02:54.210

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

00:03:01.220

Now we have, 4H equals to 20.

00:03:06.080

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

00:03:10.120

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

00:03:19.070

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

00:03:25.090

20 divides by 4, gives 5.

00:03:29.040

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

00:03:34.030

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

00:03:40.000

Therefore, the height of this parallelogram is 5 ft.

00:03:45.220

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

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