Answer:
72 cm²
Step-by-step explanation:
The diagonal of the square divides the square into 2 right triangles.
let the legs of the triangle be x , then using Pythagoras' identity.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
The hypotenuse of the triangle is the diagonal, thus
x² + x² = 12²
2x² = 144 ( divide both sides by 2 )
x² = 72 ( take the square root of both sides )
x =
The area of the square = x² = ( )² = 72 cm²