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2026-05-04 21:17:43.1777929463
What is the area of the shaded region in the circle?
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To find the area of the shaded portion of the circle, we need to find the area of the 2 segments(they are equal) and subtract that area from the area of the circle
1) lets label the points (points of the intersection of the line with the circle) on the left A and B, and the center O. Since the diameter is 12cm, then the radius is 6cm, then triangle ABC is equilateral, then The angle AOB=pi/3
2) Find the area of the sector AOB. A(AOB)=pir^2((pi/3)/2pi)=6pi 3) Find the area of the triangle AOB. A=rrsin(pi/3)1/2 = 9sqrt(3) 4) The area of the segment is 6pi-9sqrt(3) 5) The area of the circle is pir^2 = 36pi 6) and finally, the area of the shaded portion is:
A = 36pi-2*(6pi-9sqrt(3)) = 36pi-12pi+18sqrt(3) = 24pi+18sqrt(3)
Hope this helps