In the figure shown above, each inside square is formed by joining the mid points of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm² is

Correct Answer: 3.125 cm²

Step-by-Step Explanation:

1. Property of a Square Formed by Midpoints:
When a new square is formed by joining the midpoints of the sides of a larger square, the area of the new square is exactly half (1/2) of the area of the larger square.

2. Analyzing the Given Figure:
From the image provided, we can observe the nested squares starting from the outermost square down to the smallest shaded square:

• The side length of the outermost (1st) square is labeled as 10 cm.
• 1st (Outermost) Square Area:

$A_1=10\times 10=100{\text{cm}}^2$

3. Calculating Areas of Consecutive Squares:
Let us count the squares in sequence from outermost to innermost:

• 2nd Square Area (joined by midpoints of 1st square):

$A_2=\frac{100}{2}=50{\text{cm}}^2$

• 3rd Square Area (joined by midpoints of 2nd square):

$A_3=\frac{50}{2}=25{\text{cm}}^2$

• 4th Square Area (joined by midpoints of 3rd square):

$A_4=\frac{25}{2}=12.5{\text{cm}}^2$

• 5th Square Area (joined by midpoints of 4th square):

$A_5=\frac{12.5}{2}=6.25{\text{cm}}^2$

• 6th Square Area (shaded innermost square, joined by midpoints of 5th square):

$A_6=\frac{6.25}{2}=3.125{\text{cm}}^2$

Conclusion:
The area of the smallest (shaded) square is 3.125 cm².