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Area of parallelograms

Understand how to find the area of a parallelogram and why it works.

Intuition for why the area of a parallelogram is A=bh

The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.
But wait! Why are the formulas the same? Look what happens when we slide part of the parallelogram to the right.
A parallelogram and a rectangle. Both figures have the same base and height. The segment representing the height of the parallelogram is in the middle of the figure, splitting the figure in 2 parts. The rectangle is made of the same 2 parts, but with the height segment shifted right to form the side of the rectangle.
Genius! We made the parallelogram into a rectangle.
Key intuition: We can make every parallelogram into a rectangle, which is why we use the same formula to find the area of a parallelogram and a rectangle.

Practice problem 1

Find the area of the parallelogram.
A parallelogram. The segment representing the height of the parallelogram is in the middle of the figure, splitting the figure in 2 parts. The base of the parallelogram is 10 units and the height of the parallelogram is 8 units.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
square units

Practice problem 2

Find the area of the parallelogram.
A parallelogram. The segment representing the height of the parallelogram is in the middle of the figure, splitting the figure in 2 parts. The base of the parallelogram is 3 units and the height of the parallelogram is 6 units.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
square units

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