Question 16

The area of the shaded region is 0.34.

The area of the shaded region is calculated by determining the total number of shaded squares and their individual areas. Since the large square has been divided into 100 smaller squares of equal size (each with an area of 0.01), the area of the shaded region can be computed based on the number of shaded squares.

A) 0.34

This option is correct. The large square contains 100 smaller squares, and if 3 full rows of 10 squares each are shaded, that accounts for 30 squares. Additionally, there are 4 more squares shaded in the next row, bringing the total to 34 shaded squares. Since each square has an area of 0.01, the total area of the shaded region is 34 x 0.01 = 0.34.

B) 0.37

Option B is incorrect. If we consider the total number of shaded squares as calculated, there are only 34 shaded squares, which cannot yield an area of 0.37. This option does not align with the total area derived from the shading described.

C) 0.43

This option is also incorrect. The area calculation based on the number of shaded squares shows that the total shaded area does not reach 0.43. The area is limited to the 34 shaded squares, each contributing 0.01 to the area.

D) 0.7

Option D is incorrect. The calculation of shaded area based on the number of squares clearly shows that only 34 squares contribute to the total area, making it impossible for the total shaded area to be as high as 0.7. This option exceeds the computed shaded area significantly.

Conclusion

The correct answer is 0.34, as it accurately reflects the total area of the shaded squares calculated from the division of the large square into smaller squares. All other options fail to match the number of shaded squares or exceed the calculated area, demonstrating a clear understanding of the problem's geometric context.