Question

find the perimeter of a square whose area is 256 and show working

Answer 1

Given:

• Area of square = 256 cm²

To find:

• Perimeter of square.

Solution:

In order to find the perimeter of square, it's necessary to know the side of the square first. And we can find the side of the square by putting the values in the area of square, which is given by the formula:

$\boxed {\mathfrak {\pink {Area\ of\ square = s^{2}}}}$

Where,

s denotes the side of the square.

Substitute the values,

256 = s²

$\sf \sqrt{256} = s$

$\boxed {\boxed {\bf {\orange {16\ cm = side}}}}$

Now,

$\boxed {\mathfrak {\red {Perimeter\ of\ square = 4s}}}$

Substitute the values,

Perimeter = 4×16

$\boxed {\boxed {\bf {\purple {Perimeter= 64\ cm}}}}$

Perimeter of square:

Perimeter of the square is 64 cm, whose area is 256 cm².

Formulae used:

• Area of square = s²
• Perimeter of square = 4s

Answer 2

Required Answer :

$\large\sf{{{{Given}}}}$

• Area of a square = 256 cm²

$\large\sf{{{{To \: \: Find}}}}$

• Perimeter of the Square

$\large\sf{{{{Formula \: Used}}}}$

• Perimeter of Square = 4 × side

$\large\sf{{{{Solution}}}}$

To find the Perimeter of the Square, we need to first find out the Side of the Square, and to do so we need to find out the Square Root of 256, and then with the side we will be using the Formula Perimeter of Square = 4 × side to get the Perimeter of the Square, so let's do it!

√256 = side

So, the Side of the Square is 16 cm

Now, let's find out the Perimeter of the Square!

Perimeter of Square = 4 × side

Perimeter of Square = 4 × 16

Perimeter of Square = 64 cm

∴ Perimeter of the Square is 64 cm

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Important Formulas :

Perimeter of Square = 4 × side

Perimeter of Rectangle = 2 × ( Length + Breadth )

Perimeter of Triangle = Sum of all sides

Area of Square = side × side

Area of Rectangle = Length × Breadth

Volume of Cube = side × side × side

Volume of Cuboid = Length × Breadth × Height

Note : We can also write the formula Area of Square = side × side as Area of Square = ( side )² and Volume of Cube = side × side × side as Volume of Cube = ( side )³

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