Derive Area of Parallelogram

[nycmathguy]

Derive the formula A = (base)(height).

 

[MathLover1]

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.

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

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.

 

[nycmathguy]

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.

View attachment 3828


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

View attachment 3829
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.

Great notes for me. Thanks.