Find the area of a square whose diagonal is 8 cm.

The area of ​​a square (S) is equal to the product of its length and width.

A square is a rectangle in which all sides are equal, its length is equal to its width.

Therefore, S = a * a = a ^ 2, where a is the side length of the square.

To calculate the area of ​​a square, you need to know its side.

The diagonal of a square and its sides form a right-angled triangle, in which the diagonal of the square is the hypotenuse of the triangle, and the sides of the square are the legs of the triangle.

By the Pythagorean theorem, you can write:

8 ^ 2 = a ^ 2 + a ^ 2;

64 = 2a ^ 2;

32 = a ^ 2;

√32 = a.

We calculate the area of ​​a square whose side is equal to a = √32:

S = (√32) ^ 2 = 32 cm.

Answer: 32 cm.