Respuesta :
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
[tex] \boxed{\bf \:Diagonal_{(Square)} \: = side \sqrt{2}}[/tex]
On substituting the value in above formula we obtain
[tex] \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[/tex]
Therefore,
- Length of its side is 4 cm.
Finding the perimeter of square.
[tex] \boxed{\bf \: Perimeter_{(Square)} = 4 \times side}[/tex]
Substituting the value we obtain
[tex]\qquad\longrightarrow\sf \:Perimeter_{(Square)} \: = 4 \times 4 \\ \\ \\ \qquad\longrightarrow\sf \:Perimeter_{(Square)} = 16 \: cm[/tex]
Therefore,
- Perimeter of square is 16 cm .
Finding the area of square .
[tex] \boxed{\bf \: Area_{(Square)} = {side}^{2}}[/tex]
Substituting the value we get
[tex]\qquad\longrightarrow\sf \:Area_{(Square)} \: = {4}^{2} \\ \\ \\ \qquad\longrightarrow\sf \:Area_{(Square)} = 16 \: {cm}^{2} [/tex]
Therefore,
- Area of square is 16 cm².
