Finding the Area of a Parallelogram

Contributor: Ashley Nail. Lesson ID: 13102

How do you find the area of a shape that looks like this? What kind of shape IS this? Learn how to take apart parallelograms to make rectangles, and use a simple formula to find the area!

categories

Geometry, Middle School

subject
Math
learning style
Visual
personality style
Lion, Beaver
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Imagine you are a construction worker on this building:

Dockland Building City

Image [cropped] by iKLICK, via Pixabay, is in the public domain.

Your job is to replace all of the windows. You have to figure out how much glass is needed to cover the entire side of the building. Your boss says there is a way to solve this problem using skills you learned in your geometry or math class.

  • Can you think of a way to figure out how much glass you need?

If you thought "find the area," you are correct! Area is the total space inside of a flat shape.

If you were to draw an outline of the side of the building, the area would be all of the space inside of that outline. That space is full of windows that need new glass!

So, in order to figure out how much glass you need, you need to find the area of the side of the building. This would be easy if the wall were a square or a rectangle.

Let's identify the shape of the building! There are four sides, which makes it a quadrilateral. The sides are congruent. This means the sides opposite of each other are equal length. The sides are also parallel. This means the opposite sides will never touch and stay the same distance apart.

Now, do you know what shape this is?

Look at this parallelogram drawn on graph paper.

parallelogram

One way to find the area of a shape is to count the square units inside of the outline. This would be hard with a parallelogram because the units inside the outline are not all the same. Some are not full units.

However, you can take apart a parallelogram! You can break it into triangles and rectangles to help us find the area.

parallelogram

If you draw a line straight down from the top left corner, you make a right triangle. Then, if you cut that triangle off and move it to the other side of the parallelogram, it makes a rectangle!

parallelogram

Now the parallelogram has been transformed into a rectangle! This will make it easier to solve for the area!

parallelogram

Since we know that the area of a shape is all of the space inside an outline, we can now count the square units to find the area of the transformed parallelogram.

parallelogram

There are 40 square units inside the outline of the rectangle, which we proved is the same amount of space as the original parallelogram. All we did was break apart the parallelogram into triangles and rectangles. We rearranged these shapes but never changed their sizes. This is why the area of the red rectangle is the same as the parallelogram.

This means we can also find the area of a parallelogram using a formula similar to the formula used to find the area of a rectangle. The formula for the area of a parallelogram is:

Area = base x height

Look again at the parallelogram.

  • First, find the base of the parallelogram and count the units. There are eight square units along the base.
  • Next, find the height of the parallelogram. This is the number of square units from the base of the parallelogram to the top of the shape.
  • When you multiply those two numbers together, you will get the area of the parallelogram.

parallelogram

Now that you understand how to find the area of a parallelogram, head over to the Got It? section and figure out how much glass your building needs!

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