# Area of a Parallelogram

## Base times height.

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Area of a Parallelogram

Credit: bptakoma
Source: https://www.flickr.com/photos/bptakoma/3499145090

Jobie is making a lantern in his stained glass workshop. He needs to cut a piece of glass in the shape of a parallelogram that measures 6 cm in length and is 2 cm wide. What is the area of the piece Jobie will cut?

In this concept, you will learn how to find the area of a parallelogram.

### Guidance

A parallelogram is a four-sided figure, quadrilateral, with both pairs of opposite sides parallel. It doesn’t matter what the angles are in a parallelogram as long as the opposite sides are parallel.

A square is a parallelogram with all four sides equal in length and four interior 90° angles. To find the area of a square, use the formula \begin{align*}A=s^2\end{align*}.

A rectangle is a parallelogram with opposite sides equal in length and four interior 90° angles. To find the area of a rectangle, use the formula \begin{align*}A=l \times w\end{align*}.

Because a parallelogram does not have interior angles of 90°, or right angles, multiplying the length times the width does not give you the right answer. The side of a parallelogram is at an angle other than 90°. Because of this, you will need to use the base and the height dimensions in order to calculate the area.

To find the area of a parallelogram, use the formula \begin{align*}A = bh\end{align*}.

### Guided Practice

Find the area of a parallelogram with a base of 9 feet and a height of 4 feet.

First, write the formula.

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

Next, substitute in the values you have been given.

\begin{align*}A=9 \times 4\end{align*}

Then, do the multiplication.

\begin{align*}A=36\end{align*}

The answer is 36 sq. ft.

### Examples

Find the area of the following parallelograms.

#### Example 1

Base = 7 meters, Height = 3.5 meters.

First, write the formula.

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

Next, substitute in the values you have been given.

\begin{align*}A=7 \times 3.5\end{align*}

Then, do the multiplication.

\begin{align*}A=24.5\end{align*}

The answer is 24.5 sq. m.

#### Example 2

Base = 10 yards, Height = 7 yards

First, write the formula.

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

Next, substitute in the values you have been given.

\begin{align*}A=10 \times 7\end{align*}

Then, do the multiplication.

\begin{align*}A=70\end{align*}

The answer is 70 sq. yds.

#### Example 3

First, write the formula.

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

Next, substitute in the values you have been given.

\begin{align*}A=7 \times 3\end{align*}

Then, do the multiplication.

\begin{align*}A=21\end{align*}

The answer is 21 sq. in.

Credit: Steve Snodgrass
Source: https://www.flickr.com/photos/stevensnodgrass/4288992542/

Remember Jobie and his stained glass lantern?

Jobie needs to know the area of the piece below that he is cutting.

First, write the formula.

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

Next, substitute in the values you have been given.

\begin{align*}A=6 \times 2\end{align*}

Then, do the multiplication.

\begin{align*}A=12\end{align*}

The answer is 12 sq. cm.

### Explore More

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

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Color Highlighted Text Notes

### Vocabulary Language: English

TermDefinition
Area Area is the space within the perimeter of a two-dimensional figure.
Parallelogram A parallelogram is a quadrilateral with two pairs of parallel sides.
Rectangle A rectangle is a quadrilateral with four right angles.
Area of a Parallelogram The area of a parallelogram is equal to the base multiplied by the height: A = bh. The height of a parallelogram is always perpendicular to the base (the sides are not the height).