which grid has \\(\\frac{1}{2}\\) shaded?

Answer

To determine which grid has (\frac{1}{2}) shaded, we analyze each grid by counting the total number of squares and the number of shaded squares, then check if the ratio of shaded to total is (\frac{1}{2}).

Step 1: Analyze the first grid (top - left)

Assume each small square is a unit. Let's count:
- Total squares: Let's say the grid is a rectangle. If the shaded part is a (3\times2) (6 squares) and the unshaded is larger, total squares are more than 12. Shaded = 6. Ratio: (\frac{6}{\text{total}}\neq\frac{1}{2}) (since total is not 12 here).

Step 2: Analyze the second grid (top - right)

Shaded squares: Let's count the blue ones. If the grid is, say, a rectangle with rows and columns. Suppose the shaded row has 6 squares, and total squares (e.g., 3 rows of 6: 18). Shaded = 6. Ratio: (\frac{6}{18}=\frac{1}{3}\neq\frac{1}{2}).

Step 3: Analyze the third grid (bottom - left)

Let's count total and shaded. Suppose the grid has, for example, 2 rows (1 unshaded, 1 shaded) with 6 columns each. Total squares: (2\times6 = 12). Shaded squares: (1\times6 = 6). Ratio: (\frac{6}{12}=\frac{1}{2}).

Step 4: Analyze the fourth grid (bottom - right)

Shaded squares: Let's say the blue part is a (3\times2 = 6) square, and total squares (e.g., 2 sections: 6 + 6 = 12? No, if the unshaded is 6 and shaded is 6, but the layout looks different. Wait, no—if the unshaded is a (2\times3) (6) and shaded is (2\times3) (6), total is 12? Wait, no, the third grid (bottom - left) has 1 unshaded row (6) and 1 shaded row (6), total 12, shaded 6: (\frac{6}{12}=\frac{1}{2}).

So the grid with (\frac{1}{2}) shaded is the bottom - left grid (third grid in the image).