Given that, a tile is in the shape of a square.
Given that, the diagonal of a square tile is 32 cm.
The area of a square when diagonal is given = ½ d2 square units.
Now, substitute d = 32 in the formula, we get
A = (½)(32)2 square units
A = (½)(32)(32)
A = 16 × 32
A = 512 cm2
Therefore, the area of a square tile is 512 cm2.