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Area of a Parallelogram

Base times height.

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Area of a Parallelogram
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.

Finding the Area of a Parallelogram

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 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 .

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 .

Examples

Example 1

Earlier, you were given a problem about 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.

Next, substitute in the values you have been given.

Then, do the multiplication.

The answer is 12 sq. cm.

Example 2

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

First, write the formula.

Next, substitute in the values you have been given.

Then, do the multiplication.

The answer is 36 sq. ft.

Find the area of the following parallelograms.

Example 3

Base = 7 meters, Height = 3.5 meters.

First, write the formula.

Next, substitute in the values you have been given.

Then, do the multiplication.

The answer is 24.5 sq. m.

Example 4

Base = 10 yards, Height = 7 yards

First, write the formula.

Next, substitute in the values you have been given.

Then, do the multiplication.

The answer is 70 sq. yds.

Example 5

License: CC BY-NC 3.0

First, write the formula.

Next, substitute in the values you have been given.

Then, do the multiplication.

The answer is 21 sq. in.

Review

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

Review (Answers)

To see the Review answers, open this PDF file and look for section 9.9.

Resources

 

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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.

Perimeter

Perimeter is the distance around a two-dimensional figure.

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]^ License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0
  4. [4]^ License: CC BY-NC 3.0

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