Two circles A and B overlap. The overlapping (shaded) region is common to both.<br><br>&bull; Radius of A = 6.3 cm. Area of A = \( \pi r^2 = \dfrac{22}{7} \times 6.3 \times 6.3 = 124.74 \) cm&sup2;.<br>&bull; From the ratio 2 : 1 : 8, circle A is divided into shaded (2 parts) and unshaded (1 part). Total A = 3 parts.<br>&bull; 1 part = 124.74 &divide; 3 = 41.58 cm&sup2;. Shaded area (overlap) = 2 &times; 41.58 = 83.16 cm&sup2;.<br>&bull; For circle B, the same shaded (overlapping) area represents 8 proportional units from the ratio.<br>&bull; From the figure proportions, the total area of B is 4.5 times the shaded area.<br>&bull; Area of B = 4.5 &times; 83.16 = 374.22 cm&sup2;.<br><br>Final Answer: 374.22 cm&sup2;