Problem 45341. Area-06

Asif Newaz

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The length of the side of a square is given.
Draw 4 quarter-circles inside the square from 4 corners with a radius equal to the side length.
What is the area of the confined region inside(shaded region in figure).

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46 Solutions

25 Solvers

Last Solution submitted on Jan 02, 2026

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1 Comment

ChrisR on 12 Jan 2023

The image is missing at the link. This code will produce the image:

figure; hold on
plot([0 1 1 0 0],[0 0 1 1 0],'k')
t = linspace(0,pi/2); c = cos(t); s = sin(t);
c1 = c(t>=pi/6 & t<=pi/3); s1 = s(t>=pi/6 & t<=pi/3);
plot(c,s,'k',1-c,s,'k',c,1-s,'k',1-c,1-s,'k')
fill([c1 1-fliplr(c1) 1-c1 fliplr(c1)],[s1 fliplr(s1) 1-s1 1-fliplr(s1)],'y')
axis equal; box off; set(gca,'XTick',[],'YTick',[],'XColor','w','YColor','w')

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