The large square has area 1 and is divided into 25 squares of equal area. Which of the following represents the area of the shaded region?
The area of the shaded region is 0.24.
The large square has an area of 1, and when divided into 25 smaller squares of equal area, each smaller square has an area of 1/25 or 0.04. If 6 of these squares are shaded, the total shaded area is 6 * 0.04 = 0.24.
This choice suggests that the shaded region occupies 80% of the total area of the large square. However, since only 6 out of 25 smaller squares are shaded, which totals to 0.24, this option significantly overestimates the area of the shaded region.
Selecting this option implies that the shaded area is 16% of the total area. This is incorrect because 0.16 would only account for 4 of the smaller squares (4 * 0.04 = 0.16), while the problem states that 6 squares are shaded.
This is the correct choice, as the area of 6 shaded squares, each with an area of 0.04, calculates to 0.24. This represents the accurate total shaded area within the large square.
This choice suggests that the shaded area is 32% of the total area, indicating 8 shaded squares (8 * 0.04 = 0.32). However, since only 6 squares are shaded, this option overestimates the area of the shaded region.
The area of the shaded region is determined by the number of smaller squares shaded multiplied by their individual area. In this case, shading 6 squares results in a total area of 0.24, making option C the only accurate representation of the shaded area within the large square. The other choices either overestimate or underestimate the number of shaded squares, leading to incorrect values.
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