# 9.9: Area of a Parallelogram

**At Grade**Created by: CK-12

Have you ever tried to figure out the area of a figure?

Miguel is working on a problem in his math book. He has been given the following drawing.

Miguel needs to figure out the area of this parallelogram.

Do you know how to do this?

**This Concept will teach you how to figure out the area of a parallelogram. By the end of the Concept, you will know how to help Miguel with this task.**

### Guidance

Remember back to our work on quadrilaterals? Well, here is one of the quadrilaterals that we learned about earlier, the ** parallelogram**.

**A parallelogram is a four sided figure with opposite sides parallel.**It doesn’t matter what the angles are in a parallelogram as long as the opposite sides are parallel.

If we wanted to **figure out the distance around the edge of a parallelogram**, then we would find the ** perimeter** of the figure.

If we wanted to **find the measure of the space inside the parallelogram**, we would be finding the ** area** of the parallelogram. This lesson is all about finding the area of parallelograms.

Let’s start off by looking at how we find the area of a common parallelogram, the ** rectangle**.

**A rectangle is a parallelogram with four right angles. The opposite sides are parallel too.**

**To find the area of a rectangle, we multiply the length times the width.**

\begin{align*}A=lw\end{align*}

To find the area of this rectangle, we use the formula and the given measurements.

\begin{align*}A&=lw\\ A&=(6 \ in)(2 \ in)\\ A&=12 \ square \ inches \ or \ in^2\end{align*}

*Notice that the measurement is in square inches because inches \begin{align*}x\end{align*} inches is inches squared.*

*Write down the formula for finding the area of a rectangle in your notebook. Also be sure to include the statement in the box above.*

Not all parallelograms have right angles. That is why some are called squares or rectangles and some are called parallelograms. The only necessary quality of a parallelogram is that the opposite sides need to be parallel.

**How can we find the area of a parallelogram?**

Because a parallelogram does not have right angles, multiplying the length and the width is not possible. Notice that the side of a parallelogram is at an angle. Because of this, we need to use a different measure to find the area of a parallelogram. We need to use the base and the height.

Notice that the base is the bottom measurement and the height is the measurement inside the figure.

**When we multiply these two measurements, we can find the area of the parallelogram. Here is the formula.**

\begin{align*}A=bh\end{align*}

Now it's time for you to figure out the area of the following parallelograms given the base and height.

#### Example A

Base = 9 ft., Height = 4 ft.

**Solution: \begin{align*}36\end{align*} sq. ft.**

#### Example B

Base = 7 meters, Height = 3.5 meters

**Solution: \begin{align*}2.45\end{align*} sq. m.**

#### Example C

Base = 10 yards, Height = 7 yards

**Solution: \begin{align*}70\end{align*} sq. yds**

Here is the original problem once again.

Miguel is working on a problem in his math book. He has been given the following drawing.

Miguel needs to figure out the area of this parallelogram.

Do you know how to do this?

To figure this out, Miguel needs to use the formula for finding the area of a parallelogram.

\begin{align*}A = bh\end{align*}

Now we substitute the given values into the formula.

\begin{align*}A = (6)(2)\end{align*}

\begin{align*}A = 12 \ cm^2\end{align*}

**This is our answer.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Parallelogram
- a quadrilateral with opposite sides parallel.

- Perimeter
- the distance around a figure.

- Area
- the amount of space contained inside a two-dimensional figure.

### Guided Practice

Here is one for you to try on your own.

Find the area of the parallelogram below.

**Answer**

We can see that the base is 7 inches and the height is 3 inches. We simply put these numbers into the appropriate places in the formula and solve for \begin{align*}A\end{align*}.

\begin{align*}A &= bh\\ A &= 7 (3)\\ A &= 21 \ in.^2\end{align*}

**This is our answer**

### Video Review

Here is a video for review.

This is a James Sousa video on the area of parallelograms.

### Practice

Directions: Find the area of each parallelogram given the base and the height.

1. Base = 9 inches, height = 5 inches

2. Base = 4 inches, height = 3 inches

3. Base = 12 feet, height = 6 feet

4. Base = 11 meters, height = 8 meters

5. Base = 13 yards, height = 10 yards

6. Base = 4 feet, height = 2.5 feet

7. Base = 5.5 inches, height = 3.5 inches

8. Base = 9 feet, height = 6.5 feet

9. Base = 22 miles, height = 18 miles

10. Base = 29 meters, height = 12 meters

11. Base = 22 meters, height = 11 meters

12. Base = 39 meters, height = 15 meters

13. Base = 40 meters, height = 25 meters

14. Base = 88 meters, height = 50 meters

15. Base = 79 meters, height = 14 meters

### Image Attributions

Here you'll learn to find the areas of parallelograms given base and height.