The balance sheet

A unit square and a parallelogram. What’s the area of the latter?

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The parallelogram area is 1.

Solution by ajnirp.

The area of a parallelogram is base times height: so |AG| * |IC|. Now from comparing angles in right triangles ABG and CIA, they are seen to be similar. Therefore |IC|/|AC|=|AB|/|AG|. This gives |AG| * |IC| = |AB| * |AC| = 1.

Visual solution

Solution by Ben Akkus visualised by David Andriana.


We live and die
In between
Our heart is beating
Our soul willing
Our brain thinking
We are working
We have friends and values
Living with moral and love
We are dreaming
And loving
(inspired from Balance sheet of life, author unknown)


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One reply on “The balance sheet”

First glide the parallelogram’s top edge until the adjacent edges are vertical. This doesn’t change area. Then glide left edge down until you have the square. Again the area doesn’t change.

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