Question

the diagonal of a square is 12 cm long find its area and perimeter​

Answer 1

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Given ,

$\star$Diagonal of square = 12 cm

Now ,

$\fbox{ \large \fbox{ \sf \: Diagonal \: of \: square = \sqrt{2} \times side \: \: }}$

$\implies \sf 12 = \sqrt{2} \times Side \\ \\ \implies \sf Side = \frac{ 12 }{ \sqrt{2} } \\ \\ \implies \sf Side = 6 \sqrt{2} \: \: cm$

$\large \sf \fbox{ \fbox{Area \: of \: square = {(side )}^{2} }}$

$\sf \implies Area = {(6 \sqrt{2} )}^{2} \\ \\\sf \implies Area = 36 \times 2 \\ \\\sf \implies Area = 72 \: \: {cm}^{2}$

$\large \sf \fbox {\fbox{Perimeter \: of \: square = 4 × side}}$

$\implies \sf Perimeter = 4 \times 6 \sqrt{2} \\ \\ \implies \sf Perimeter = 24 \sqrt{2} \: \: cm$

$\therefore$Area of square = 72 cm² and Perimeter of square = 24√2 cm

Answer 2

Answer:

Area of square = 1/2 (d)²

= 1/2 (12)²

= 1/2 × 12 × 12

= 72 cm sq

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

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Step-by-step explanation: