Question

In the figure, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest shaded square is to be found. The outermost square has a side length of 10 cm. 

• A. 12.50
• B. 6.25
• C. 3.125
• D. 1.5625

Hint:

Joining midpoints of a square always produces a new square with exactly half the area of the previous one.

Answer 1

The Correct Option is C

Joining midpoints of a square forms a new square whose area is exactly half of the previous square.

Step 1: Area of the outermost square.
Side = 10 cm → Area = \(10^2 = 100\) cm².

Step 2: Area ratio for midpoint-joined squares.
Each new square = \( \frac{1}{2} \) × area of previous square.
Thus areas form the sequence: \[ 100,\; 50,\; 25,\; 12.5,\; 6.25,\; 3.125,\; \dots \]

Step 3: Identify the smallest shaded square.
According to the diagram, the smallest (innermost) shaded square corresponds to \[ 100 \times \left(\frac{1}{2}\right)^5 = 3.125. \]

Final Answer: 3.125