Answer:
72 cm
Step-by-step explanation:
You can solve this problem using the properties of the 45-45-90 right triangle. Assuming the 12 cm is a diagonal of the square, each side of the square can be modeled as x, and the diagonal will be x.
This means , so
.
Next, to find the area of the square you take the square of any of its sides. Since x is the length of one side, and , you can square
to get the area. This is equal to
or 72 cm.