1.

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

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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


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