Question

The diagonal of a square is 4 cm . Find it's area.

Answer 1

let a square of side a

then it's diagonal by Pythagoras theorem=√2 a

given diagonal =4

√2 a = 4

a= 2√2 cm

now area of square = side × side

= 2√2 × 2√2

= 8 cm ^2

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Answer 2

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Answer:

It is given that diagonal BD= 4 cm(See the enclosed figure)

Let each side of the square be 'a'.

Here, ∆BAD and ∆BCD are right triangles (ABCD is a square).

Now, applying Pythagoras theorem in ∆ABD,

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

(BD)²= (AB)²+(AD)²

(4)²= (a)²+(a)²--------(All the sides of a square are equal )

16= 2a²

16÷2= a²

8= a²

2√2 cm= a

Thus, each side of the square is of length 2√2 cm

Now, Area of a square= a² where a is the side

=> (2√2)²

=> 4×2

=> 8 cm²

Answer=> 8 cm²