Question

Find the area of the crescent-shaped region (called a lune) bounded by arcs of circles with radii r = 2 and r = 14

Answer 1

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-A2

A1=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