Final answer:
To calculate the area of a square with a diagonal of 5 cm, divide the diagonal length by the square root of 2 to find the side length, square this length to find the area, resulting in approximately 12.52 cm².
Step-by-step explanation:
The student is asking for the area of a square given the length of its diagonal is 5 cm. To find the area of the square, we can use the knowledge that the diagonals of a square cut it into two right-angled triangles with the sides of the square being the legs. Since the diagonal d of a square divides it into two 45-45-90 triangles, and using Pythagoras' theorem, we can find the length of one side, a, with the formula a = d/√2. In this case, a = 5 cm/√2 ≈ 3.54 cm (rounded to two decimal places). Then the area A is given by A = a² = (3.54 cm)² ≈ 12.52 cm².