The length BC is the length of an arc subtended by angle 120 degrees at the center of a circle of radius 5. Recall that the length of an arc, l, subtended by an angle, x degrees, in the center is given by l = 120 / 360 x pi x 2r Thus, BC = 120 / 360 x 3.14 x 2 x 5 = 10.4667 Similarly, length DA is the length of an arc subtended by angle 30 degrees at the center of a circle of radius 5.Thus, DA = 30/360 x 3.14 x 2 x 5 = 2.6167 Therefore, the approximate length of boundary ABCD = 5 + 10.4667 + 5 + 2.6167 = 23.0834 = 23.1 to one decimal place.
