area of a trapezoid Best Solution to "Octagon in the Parallelogram" (MindYourDecisions)

This is the best Geometric and (Non-Algeberaic) answer to MindYourDecision's Math problem from Russia. " https://www.youtube.com/watch?v=rwDgf...

Question is, Draw any Parallelogram. Connect every corner with the mid points of every side. In the center you will have an Irregular Octagon. What proportion of area does that Octagon hold, to the Parallelogram?

Best Geometric Method.
Algebraic version is even simpler.

The most complete answer would be to multiply my final answer by 4 (for the 4 quadrants of the octagon) and divide by 4 (for the 4 quadrants of the square).. realize they cancel... And THEN circle the 1/6. I skipped the step already knowing this.,

area of a trapezoid Best Solution to "Octagon in the Parallelogram" (MindYourDecisions)
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