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0 sats \ 5 replies \ @Scroogey 14 Dec 2024 \ parent \ on: [Not-so-daily puzzle] Purple area science
I guess the question is, are the green lines intersecting chords through one and the same point?
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If we look at the upper blue region:
The area is the sum of the components:
A = g * (t + \frac{s}{2}) + u*s + u*tAdding the same (with
h instead of g) for the lower blue region:38 = (g+h)*(t + \frac{s}{2}) + 2*u*s + 2*u*tThe apothem formula gives
tan(\frac{\pi}{24})*(g+h+2*u) = sSimple trig says
t = s*cos(15°)u = s*sin(15°)Those last four equations solve for
s \approx 1.82625, or total area of polygon A=152.As seen in @0xbitcoiner's drawing, the total area is the sum
38 + 47 + 47 + 2 * x = 152Therefore,
x = 10reply
I'm not going to be the one checking those calculations! 😎👍
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Correct, the area of the magenta region equals $10$.
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