Question

If the length of diagonal of a square is 4√2 cm, find it's length, perimeter and area.​

Answer 1

Answer:

As Per Provided Information

• Length of diagonal of square is 4√2 cm

We have been asked to find the length , perimeter and area of square .

First let's calculate the side of square .

Using Formulae

$\boxed{\bf \:Diagonal_{(Square)} \: = side \sqrt{2}}$

On substituting the value in above formula we obtain

$\qquad\longrightarrow\sf \:4 \sqrt{2} = side \sqrt{2} \\ \\ \\ \qquad\longrightarrow\sf \:4 \cancel{\sqrt{2}} = side \cancel{ \sqrt{2}} \\ \\ \\ \qquad\longrightarrow\sf \:side \: = 4 \: cm$

Therefore,

• Length of its side is 4 cm.

Finding the perimeter of square.

$\boxed{\bf \: Perimeter_{(Square)} = 4 \times side}$

Substituting the value we obtain

$\qquad\longrightarrow\sf \:Perimeter_{(Square)} \: = 4 \times 4 \\ \\ \\ \qquad\longrightarrow\sf \:Perimeter_{(Square)} = 16 \: cm$

Therefore,

• Perimeter of square is 16 cm .

Finding the area of square .

$\boxed{\bf \: Area_{(Square)} = {side}^{2}}$

Substituting the value we get

$\qquad\longrightarrow\sf \:Area_{(Square)} \: = {4}^{2} \\ \\ \\ \qquad\longrightarrow\sf \:Area_{(Square)} = 16 \: {cm}^{2}$

Therefore,

• Area of square is 16 cm².