Find the area of a square whose diagonal is 3.

1. Vertices of the square A, B, C, D. Diagonal AC = 3 units.

2. The diagonal AC is the hypotenuse of the right-angled triangle ACD.

3. Let’s compose the equation using the formula of the Pythagorean theorem:

AD² + CD² = AC²

4. Take as x the length of the side of the square.

x² + x² = 9;

2x² = 9;

x² = 9/2;

x = √9 / 2 = 3√2 / 2 units.

5. Calculate the area (S) of the square:

S = 3√2 / 2 x 3√2 / 2 = 4.5 units².

Answer: the area of a square is 4.5 units of measurement².