CBSE Class 10 Answered

DB = 6 cm

DE = EB = 6/2 = 3 cm

DG = radius = 6 cm.

Hence GE = 33 cm, using Pythagorus's theorem in DEG,

sin EDG = 3/2

 EDG = 60

 FDG = 2x60 = 120

Area of segment GBF = Area of sector DFBG - Area of triangle DFG

= πR²/3 - (1/2)(R/2)(3R)

= 22.09 sq. cm.

Area of region GEB = 22.09/2 = 11.05 sq cm.

Area of region DEBG = 2xArea of region GEB = 22.09 sq. cm.

Shaded are of one part of the total black shaded area = (1/4) area of circle with radius R - Area of region DEBG

= (1/4)(3.14)(36) - 22.09 = 6.17 sq cm.

REQUIRED SHADED AREA = 2X6.17 = 12.34 sq cm.

Regards,

Team,

TopperLearning.