B

Step 2: In a square, all the sides are equal and each angle is equal to 90^o.

Step 3: So, a right triangle is formed by the diagonal of the square as hypotenuse and the sides of the square as the legs of the right triangle.

Step 4: Hypotenuse² = sum of the squares of the legs[Pythagorean theorem]

Step 5: Let a be the side of the square.

Step 6: Diagonal² = a² + a²[Diagonal is hypotenuse and sides are legs of the right triangle.]

Step 7: Diagonal = √(2a²)[Add and take square root on both sides.]

Step 8: So, diagonal = a√2[Simplify.]

Step 9: 2√2 = a√2[Substitute diagonal of the square.]

Step 10: 2 = a[Divide both sides by √2.]

Step 11: Area of the square = a²[Formula : area of square = side².]

Step 12: [Substitute a = 2 and simplify.] = 2 x 2 = 4

Step 13: So, area of the square = 4 in.²