Outside the box
In the image above we have a circle with a diameter of 40.
The equilateral triangle ABC is inscribed in this circle.
Square DEFG is inscribed in triangle ABC.
Calculate the total area of the red shaded areas.
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1 solution
Red Area
= r²(π/4 - 1/2) + 2r²[π/12 - (sin 30°)/2]
= r²(5π/12 - 1)
For r = 30(√8 - √6),
Red Area ≈ 40