Question

The length of the diagonal of a square is 3 cm . Find (i) The area of square (ii) the perimeter 2 decimal places​

Answer 1

ANSWER:

• Area of Square = 4.5 cm²
• Perimeter of Square = 8.48 cm

GIVEN:

• length of diagonal of square = 3cm

TO FIND:

1. Area of square
2. Perimeter of Square. (upto 2 decimal places)

SOLUTION:

Formula:

Diagonal of a Square = √2(Side of square)

Now

$\implies \: 3 = \sqrt{2} (side) \\ \implies \dfrac{3}{ \sqrt{2} } = side \: \\ \implies \: \dfrac{3}{ \sqrt{2} } \times \dfrac{ \sqrt{2} }{ \sqrt{2} } = side \: of \: square \\ \implies \: \dfrac{3 \sqrt{2} }{2} = \: side \: of \: square$

Area of square = (Side)²

$\implies \: area \: of \: square = ( \dfrac{3 \sqrt{2} }{2} ) {}^{2} \\ \implies \: area \: = \dfrac{9 \times 2}{4} \\ \implies \: area \: = \frac{9}{2} cm {}^{2} \\ \implies \: area \: = \: 4.5 \: cm {}^{2}$

Perimeter of Square = 4(Side)

$\implies \: perimeter \: = 4 \times \dfrac{3 \sqrt{2} }{2} \\ \implies \: perimeter \: = 6 \sqrt{2} \: cm \\ \implies \: perimeter \: = 6 \times 1.414 \\ \implies \: perimeter \: = \: 8.484 \: cm \\ \implies \: perimeter \: = 8.48 \: cm$

Answer 2

Answer:

refers to the attachment