Grade 10 Math · Area in reverse
Running the machines backwards
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Running the machines backwards

So far the area was the answer. Now it's a GIVEN, and a side is hiding. Working backwards is division: a rectangle's width is w=Alw = \dfrac{A}{l}; a triangle's height is h=2Abh = \dfrac{2A}{b}, the ½ un-halving into a 2 on top, exactly as last lesson promised.

Circles add one more move. A=πr2A = \pi r^2 reversed gives r=Aπr = \sqrt{\dfrac{A}{\pi}}r equals the square root of A over pi: divide the π\pi away first, then un-square with the root. Dividing by π\pi leaves r2r^2, and r2r^2 is not yet rr — stopping there is this lesson's favourite trap. The draws are kind: every root lands on a perfect square.