In the figure shown, each side of the outer square is divided into four equal segments. The shaded square in the middle is of area 18 unit2. What is the area of the outer square?Options14442None of these250

To solve this problem, we need to understand that the area of a square is calculated by squaring the length of one of its sides.

Step 1: Find the side length of the shaded square. Since the area of the shaded square is 18 square units, its side length is the square root of 18, which is approximately 4.24 units.

Step 2: Determine the proportion of the shaded square's side length to the side length of the outer square. From the figure, we can see that the side length of the shaded square is equivalent to 2 segments of the outer square's side. Since the outer square's side is divided into 4 equal segments, the side length of the outer square is twice that of the shaded square.

Step 3: Calculate the side length of the outer square. Since the side length of the outer square is twice that of the shaded square, it is 2 * 4.24 = 8.48 units.

Step 4: Calculate the area of the outer square. The area of a square is calculated by squaring the length of its side, so the area of the outer square is (8.48)^2 = 71.86 square units.

Therefore, the area of the outer square is approximately 72 square units. The closest option to this value is 42, so the correct answer is "None of these".