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Area of a Parallelogram

Base times height.

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Area of a Parallelogram

Let’s Think About It

Credit: bptakoma
Source: https://www.flickr.com/photos/bptakoma/3499145090
License: CC BY-NC 3.0

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 A=s2.

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 A=l×w.

License: CC BY-NC 3.0

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 A=bh.

Guided Practice

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

First, write the formula.

A=bh

Next, substitute in the values you have been given.

A=9×4

Then, do the multiplication.

A=36

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.

A=bh

Next, substitute in the values you have been given.

A=7×3.5

Then, do the multiplication.

A=24.5

The answer is 24.5 sq. m.

Example 2

Base = 10 yards, Height = 7 yards

First, write the formula.

A=bh

Next, substitute in the values you have been given.

A=10×7

Then, do the multiplication.

A=70

The answer is 70 sq. yds.

Example 3

License: CC BY-NC 3.0

First, write the formula.

A=bh

Next, substitute in the values you have been given.

A=7×3

Then, do the multiplication.

A=21

The answer is 21 sq. in.

Follow Up

Credit: Steve Snodgrass
Source: https://www.flickr.com/photos/stevensnodgrass/4288992542/
License: CC BY-NC 3.0

Remember Jobie and his stained glass lantern?

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

License: CC BY-NC 3.0

First, write the formula.

A=bh

Next, substitute in the values you have been given.

A=6×2

Then, do the multiplication.

A=12

The answer is 12 sq. cm.

Video Review

https://www.youtube.com/watch?v=npY54EKjWaA

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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Vocabulary

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).

Image Attributions

  1. [1]^ Credit: bptakoma; Source: https://www.flickr.com/photos/bptakoma/3499145090; License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0
  4. [4]^ Credit: Steve Snodgrass; Source: https://www.flickr.com/photos/stevensnodgrass/4288992542/; License: CC BY-NC 3.0
  5. [5]^ License: CC BY-NC 3.0

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