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Lesson 2: Area of parallelograms and triangles

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 $A=bh$A, equals, b, h

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.
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.
square units

Practice problem 2

Find the area of the parallelogram.
square units

Want to join the conversation?

• why does it not count when the number is curve
• If it was carved it can’t have a number
• Would it still work if it wasn't drawn to scale? Also, are you not just multiplying the numbers, or is there more to it?
• Another way of thinking why it will work is that a Parallelogram has 2 pairs of sides that are of equal length (Opposite sides have equal length).

Therefore, the parallelogram will always be able to fit into a rectangle when rearranged properly => Formula of finding the area of a rectangle will work as long as we are sure that the figure that we are handling is truly a parallelogram irregardless of whether it is drawn to scale or not.
• How come they did not put a multiplication sign, they just put bh? shouldn't there be multiplication sign?
• putting bh is the same as b • h or b x h
• this is confusing
• if there will be only two numbers multiply those or act like the shape provided can be turned into a square then do it like it is a square.
• what is with the extra third number when practicing? like for example we are timesing the base and height (10 x 14 = 140) but there is a third number outside the parallelogram? we just basically ignore it?
• A third number will usually be measuring the length of one of the diagonal sides. I would have to see the specific example to be sure though.
• how do you make the area of any quadrilatarel
• Area = L x W. literally all you need to know, but if you don't know how to do the math, think of length as jumping, and that width is running, the same way my 5th-grade teacher taught me with coordinate and quadrant planes
• why is there a third number if we are just timing the base and height