Question 1

The area of the shaded region is 0.24.

The area of the shaded region can be determined by calculating the area of the large square and then finding the area of the unshaded parts. Given that the large square has an area of 1 and is divided into 25 smaller squares, each smaller square has an area of 0.04. If 6 squares are unshaded, the total unshaded area is 0.24.

A) 0.8

Option A is incorrect because 0.8 exceeds the total area of the large square, which is 1. If 0.8 were the area of the shaded region, it would imply that the unshaded area is only 0.2, which is not feasible given the distribution of the smaller squares.

B) 0.16

Option B is incorrect. If the shaded area were 0.16, the remaining unshaded area would be 0.84, which again exceeds the total area of the large square. The calculations of shaded versus unshaded do not support this figure based on the division into 25 equal squares.

C) 0.24

Option C is correct as it accurately represents the area of the shaded region. With each of the 25 squares having an area of 0.04, if 6 squares are unshaded, the area of the unshaded squares is 6 * 0.04 = 0.24, confirming that the shaded area is indeed 0.24.

D) 0.32

Option D is incorrect because an area of 0.32 for the shaded region would suggest that the unshaded area is only 0.68. This scenario is impossible, as it would mean 8 squares are unshaded (8 * 0.04 = 0.32), which contradicts the problem's parameters.

Conclusion

In this context, the correct answer is definitively 0.24, as it logically follows from the division of the large square into smaller squares and the calculation of shaded versus unshaded areas. All other options fail to align with the total area of the square and the correct distribution of the smaller squares.