Question 8
Quang starts with a square of area $256\text{ cm}^2$ (Figure 1). He adds four squares at its four corners, each with one quarter of its area (Figure 2). Next, at the three outward corners of each newly added square, he adds three more squares, each having one quarter of that square’s area (Figure 3). He repeats this rule to obtain Figure 4 and continues in the same way. What is the total area of all the shaded squares in Figure 6, in square centimetres?
