Derive Area of Parallelogram

Discussion in 'Other Pre-University Math' started by nycmathguy, Jul 7, 2022.

  1. nycmathguy

    nycmathguy

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    Derive the formula A = (base)(height).
     
    nycmathguy, Jul 7, 2022
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  2. nycmathguy

    MathLover1

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    To derive the formula for the area of a parallelogram moving a piece of the parallelogram so as to make a rectangle with the same area.

    Start with a parallelogram with known base length (width) w and altitude h (height). Cut off a triangular section.

    upload_2022-7-6_21-46-14.jpeg


    Translate (move) the copy to touch the original so as to create a rectangle.

    upload_2022-7-6_21-47-14.jpeg
    This rearranging has created a rectangle whose area is clearly the same as the original parallelogram. Recall that the area of a rectangle is found by multiplying its width times its height. The area of the original parallelogram is therefore area of parallelogram is
    A=w*h
    where w is the width, or length of a base, and h is the altitude (height) of the parallelogram.
     

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    MathLover1, Jul 7, 2022
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  3. nycmathguy

    nycmathguy

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    Great notes for me. Thanks.
     
    nycmathguy, Jul 7, 2022
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