The area of square with diagonal 10 cm is:

1. 100 cm²

2. 50 cm²

3. 25 cm²

4. 75 cm²

Given:

The diagonal of the square is 10 cm.

Let each side of the square be a cm.

Then, by using the Pythagoras theorem,

⇒ Diagonal² = Side² + Side²

⇒ (10)² = a² + a²

⇒ 100 = 2a²

⇒ a² = $\dfrac{100}{2}$

⇒ a² = 50

⇒ a = $\sqrt{50}$

⇒ a = 5 $\sqrt{2}$

As we know, the area of a square = side²

= (5 $\sqrt{2}$) ² cm²

= 25 x 2 cm²

= 50 cm²

Hence, option 2 is the correct option.