How to calculate the Yellow Area? | Square and Quarter Circle | Tricky GeoGebra Math Problem

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My solution was the exact same as yours, even used the same variable names, but unfortunately i found a much cheaper way to solve:

No lengths are given besides that 4 so i can assume no matter where that 4 is the area will be the same (otherwise this wouldnt be a math question) so i just let it go from corner to corner, solve r = 2sqrt2 with pythagorean and then square that and get 8 for area.

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Let the radius be r, then the area of the shaded is r*4cos x, where x is the angle between the red line and the horizontal radius. But rcos x=4/2 =2 because two radii and the red line form an isosceles triangle with base angles equal to x.

wychan