Area of parallelograms

Teaser and introduction goes here. Sample problem here.

Finding the area of parallelograms means you need to count the number of unit squares inside the parallelogram. This is a bit more difficult than the rectangle since the parallelogram cuts many of the unit squares into fractional pieces.

However, we can rearrange the parallelogram into a more familiar figure without changing its original area. Then we can find the area of the familiar figure, which will have the same area as the parallelogram.

 

In this parallelogram, you can cut the triangle from the left of the parallelogram and move it to the right side of the parallelogram, making a rectangle. We know the formula for finding the rectangle’s area is baseheight, so the area of this shape is 8 • 5, which is 40 square units.

Basically, to find the area of a parallelogram you use the same formula as with rectangles.

A = baseheight

A = bh

Notice that the lengths of the slanted sides of the parallelogram do not have any affect on the area of the parallelogram.

 


 

Find the area of this parallelogram.

A = bh

A = (5)(2)

A = 10 u^2

 


 

Find the area of this parallelogram.

A = bh

A = (6)(3)

A = 18 u^2

 

 

  

Directions:

  1. Move line m and n to change the height of the rectangle and the parallelogram.
  2. Move point C to change the base fo the figures.
  3. Move point E to alter the slant of the parallelogram.
  4. Regardless of how much the parallelogram slants, what do you notice about the areas?
  5. How does the area of the rectangle compare with the area of the parallelogram that has the same bse and height?

 

 


 

Directions:

  1. Move lines b and c to change the height.
  2. Move the left blue point to change the slant of the parallelogram.
  3. Move the right blue point to change the base of the parallelogram.
  4. Pull the animation slider to see how the area of a parallelogram compares with the area of a rectangle.

 

 


Self-Check


Question 1

Find the area of this parallelogram.

 

[show answer]


Question 2

Find the area of this parallelogram.

 

[show answer]


Question 3

Find the area of this parallelogram.

 

[show answer]