Question

(b) If the length of a diagonal of a square is
16 cm then what is it's area​

Answer 1

Answer :-

The area of square is 127.91cm.

Step-by-step explanation:

To Find :-

• The area of square.

★ Solution

Given that,

• The diagonal of square = 16cm.

FIGURE :-

• Refer the attachment.

∴ The side of square :-

We can find out the side of square by applying the formula of "diagonal of square" :-

We know,

Diagonal of square = s√2,

Where,

s = side of square

Therefore,

⇒ s√2 = Diagonal

⇒ s√2 = 16

⇒ s = 16/√2

⇒ s = 11.31cm

The side of square is 11.31cm.

_____________________________

Now, According the question,

• The area of square :-

We know,

Area of square = (s)² sq. units,

Where,

s = side of square

Therefore,

⇒ (s)²

⇒ (11.31)²

⇒ 11.31*11.31

⇒ 127.91cm² ★

Hence,

The area of square is 127.91cm².

Answer 2

128 cm²

Step-by-step explanation:

Given -

Diagonal of a square is 16 cm

To find -

Area of square

Solution -

Diagonal = side × √2

=> 16 cm = side × √2

=> 16/√2 cm = side

=> side = 16/√2

Area of square = side × side

=> (16/√2) × (16/√2) cm²

=> (16×16)/(√2×√2) cm²

=> 256/2 cm²

=> 128 cm²

Hence area of square = 128 cm²

hope it helps.