Math Puzzle: Where is the Missing Area?

The square below is made up of two triangles and two trapezoids. The dimensions of the square is 13 by 13, which means that the area is 169 square units.

missing-area-1

The same polygons above are used to create the rectangle below. The dimensions of the rectangle is 8 by 21, which means that the area is 168.

missing-area-2

Wait! Aren’t they supposed to have the same areas? We did not add are cut anything right?  Where do you think is the missing area?

If you want to explore more, the dynamic version of the missing area puzzle can be found here. Note that your computer must have Java to run the animation.

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