Find the area of a square whose diagonal is 6 cm.

1. Vertices of the square A, B, C, D. AC – diagonal.

2. The sides of the square are equal to each other. Therefore, AD = CD. These sides are the legs of the right-angled triangle ACD, and the diagonal AC is the hypotenuse.

3. We take the length of each side АD and СD for x (cm).

4. Let’s compose an equation using the Pythagorean theorem:

x² + x² = 6²;

2x² = 36;

x² = 18;

x = √18 cm.

4. Calculate the area (S) of a given geometric figure:

S = √18 x √18 = 18 cm².

Answer: the area of the square is 18 cm².