Question

The length of the diagonal of square is 10√2 . It's area is​

Answer 1

The diagonal of square = √2side

10√2 = √2side

side = 10√2/√2

side = 10

Area = side^2

Area = 10*10

Area = 100 square unit

Answer 2

Given :

• Length of the diagonal of square = 10√2

To Find :

• Area of the square.

Solution :

Let the side of the square be a. We know that all the sides are equal of square.

Applying Pythagoras Theorem :

★ (Hypotenuse)² = (Perpendicular)² + (Base)²

→ (10√2)² = (a)² + (a)²

→ 100 × 2 = a² + a²

→ 200 = 2a²

→ a² = $\sf\cancel\dfrac{200}{2}$

→ a² = 100

→ a = √100

→ a = 10 units

We've obtained the side of square, let's find area now.

★ Area of Square = (Side)²

→ (10)²

→ 10 × 10

→ 100 units.

$\therefore$ Area of the square is 100 units.