Question

the parimetre of a square is 28 cm find the area and length of diagnal​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\blue{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\green{Given:}}}}}$

• the Perimetre of a square is 28 cm

$\bf{\underline{\underline{\sf{\green{To\:find:}}}}}$

• Area of Square
• Length of the diagonal

$\bf{\underline{\underline{\sf{\green{Solution:}}}}}$

Let the side of the square be x cm

We can find the length of the side of Square using the formula for perimeter of a square.

$\bf{\large{\underline{\boxed{\sf{\pink{Perimeter\:of\:a\:square\:=\:4\:\times\:side}}}}}}$

Plug in the values,

=> ${28 = 4\:\times\:side}$

=> ${28 = 4\:\times\:x}$

=> $\large\frac{28}{4}$ = ${x}$

=> $\large\frac{14}{2}$ = ${x}$

=> ${7\:=\:x}$

Side of the square = x = 7 cm

Now as we have calculated the side of the square, it becomes pretty simple to find the area and length of the diagonal using the formulae.

We know that the area of square is calculated using the formula,

$\bf{\large{\underline{\boxed{\sf{\pink{Area\:of\:a\:square\:=\:side^2}}}}}}$

Plug in the values,

=> ${Area\:=\:side\times\:side}$

=> ${Area\: =\:7\:\times\:7}$

=> Area = 49 sq.cm

Now using the formula,

$\bf{\large{\underline{\boxed{\sf{\pink{Area\:of\:a\:square\:=\frac{1}{2}\times\:(diagonal)^2}}}}}}$

Plug in the values,

=> 49 = ½ × diagonal²

=> 49 = $\frac{diagonal^2}{2}$

Cross multiplying,

=> 49 × 2 = diagonal²

=> 98 = diagonal²

=> $\sqrt{98}$ = diagonal

=> 9.8 = diagonal (approx.)

$\bf{\large{\underline{\boxed{\sf{\blue{Area\:of\:square\:=\:49\:cm^2}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\blue{Length\:of\:diagonal\:=\:9.8cm}}}}}}$

Answer 2

$\huge{\mathfrak{\underline{\underline{\red{AnswEr :-}}}}}$

Given :-

Perimeter of square is 28 cm.

To Find :-

Area of square

Length of Diagonal

Solution :-

Let the side of the square be a.

$\huge{\sf{\large{\underline{\boxed{\blue{Perimeter\:of\:a\:square\:=\:4\:\times\:side}}}}}}$

______________[Put Values]

28 =.4 × side

28 = 4 × a

28/4 = a

7 = a

Side of the square = a = 7cm

Using Formula

$\huge{\underline{\boxed{\sf{\blue{Area\:of\:a\:square\:=\:side^2}}}}}$

___________[Put values]

Area = (7)²

Area=7 × 7

Area = 49 cm²

Using Formula

$\huge{\underline{\boxed{\sf{\pink{Area\:of\:a\:square\:=\frac{1}{2}\times\:(diagonal)^2}}}}}$

_____________[Put values]

49 = 1/2 × diagonal²

49 × 2 = diagonal²

98 = diagonal²

√98 = diagonal

Put value of √98 as 9.8

9.8 = diagonal (approx)

$\huge{\boxed{\orange{\underline{ Area = 49 cm^{2}}}}}$

$\huge{\boxed{\orange{\underline{ Diagonal = 9.8 cm}}}}$