Question

The diagonal of a square is 12 cm long.Find its perimeter and area

Answer 1

let sides of the squares be "a"
 diagonal of a square forms two right angle triangle
take one triangle from them and apply Pythagoras theorem 
so the diagonal will be the hypotenuse 

$12^{2}$ = a $a^{2}$ + $a^{2}$

144 = $2a^{2}$

144÷2 = a$a^{2}$

$\sqrt{72}$ = a

area of square is $a^{2}$

$a^{2}$ = 72

perimeter of square is 4a

$4 \sqrt{72}$

Answer 2

Solution: 

Diagonal of a square = 12 cm 

Area of square = 1/2 (d)² 

                         = 1/2 (12)² 

                         = 1/2 × 12 × 12 

                         = 72 

Side of a square = √Area

                           = √72

                           = √(2 × 2 × 2 × 3 × 3) 

                           = 2 × 3√2

                           = 6 × 1.41

                           = 8.46 cm

Perimeter of square = 4 × 8.46 = 33.84 cm