Question 13

The area of the shaded region is 0.32.

The large square has an area of 1, and it is divided into 25 smaller squares of equal area, meaning each small square has an area of 0.04. The shaded region consists of 8 of these smaller squares, resulting in a total area of 0.32.

A) 0.8

This option is incorrect because 0.8 exceeds the total area of the large square, which is only 1. Even if all 25 squares were shaded, the maximum area would still only equal 1, making 0.8 impossible for the shaded area.

B) 0.16

This option is also incorrect. If 0.16 were the area of the shaded region, it would imply that 4 of the smaller squares were shaded (since 4 squares of area 0.04 equal 0.16). However, this does not align with the information provided regarding the actual number of shaded squares.

C) 0.24

This option is incorrect as well. The area of 0.24 would suggest that 6 small squares are shaded (6 squares of area 0.04 total 0.24), but this does not correspond to the actual count of shaded squares in the problem.

D) 0.32

This is the correct option, as it accurately represents the area of the shaded region. With 8 small squares shaded, the calculation is straightforward: 8 squares x 0.04 area per square equals 0.32.

Conclusion

The correct answer, 0.32, clearly reflects the actual area of the shaded region, derived from the precise count of shaded small squares. Options A, B, and C fail to represent the shaded area accurately based on the given information, thus confirming D as the only valid choice.