Find the length of the arc L if angle β = 111 degrees

The side of the equilateral triangle, S,   will   =   the radius of the  circle

Area of equilateral  triangle  = (sqrt(3) /4) S^2

10  = (sqrt (3) / 4 ) * S^2

10 * 4  /sqrt (3)  =  S^2

40 / sqrt (3)  = S^2       take the square  root  of both sides

S =  sqrt (40) / (3)^(1/4)  = S =  circle radius

arc length =  2pi  * R *  [ central angle measure /  360)  =      2pi * [ sqrt (40 / 3^(1/4) ]   (111/ 360 ) ≈    9.31 cm