Find the area of the crescent-shaped region (called a lune) bounded by arcs of circles with radii r = 2 and r = 14
1 answer:
the complete question in the attached figure
Let
A1-------> half of the area of the blue circle
A2-------> area of the circular segment formed by the diameter of the blue circle treated as a chord of the red circle
A3---------- > area of the crescent-shaped region
A3=A1-A2A1=pi*2²/2=6.28
Area of the circular sector
if 360 º corresponds to an area of pi*14²
2*arc sin(2/14)------------------- X
X=16.43*pi*14²/360---------- > X=28.10
Triangle area:
------- >(4/2)*√(14²-2²=27.72
Area of the circular segment A2=Area of the circular sector-Triangle area
A2=28.10-27.72=0.38
A3= A1-A2=6.28-0.38=5.90 units²
the answer is 5.90 units²
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