Question

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Answer 1

Question 1:

The diagonal of a square is 5√2 m. Find its area and perimeter.

★ Formulae to be Used:

→ $\sf{\boxed{Diagonal=\sqrt{2}\times\:side}}$

→ $\sf{\boxed{Area\:of\:square=a^2}}$

→ $\sf{\boxed{Perimeter\:of\:square=4a}}$

★ Solution:

Diagonal of the square = 5√2.

We know that the diagonal of a square = √2 x side

So,

Side of the given square = 5 x √2

= 5 m

Area of a square = a²

= 5²

= 5 x 5

= 25 m²

Perimeter of a square = 4a

= 4 x 5

= 20 m

★ Final Answers:

Area of the square = 25 m²

Perimeter of the square = 20 m

Question 2:

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

★ Formulae to be Used:

→ ${\sf{\boxed{Area\:of\:square=\dfrac{1}{2}\times\:d^2}}}$

→ $\sf{\boxed{Side=\sqrt{Area}}}$

→ $\sf{\boxed{Perimeter=4a}}$

★ Solution:

Diagonal of the square = 12 m

Area of a square = 1/2 x d²

$\sf{=\dfrac{1}{2}\times12^2}$

$\sf{=\dfrac{1}{2}\times144}$

$\sf{=72\:m^2}$

Area = 72 cm²

Side of a square = √Area

$\sf{=\sqrt{72}}$

→ As we cannot find the root directly, we must find the factors of 72.

$\sf{=\sqrt{3\times3\times2\times2\times2}}$

→ Taking out the common factors:

$\sf{=3\times2\sqrt{2}}$

$\sf{=6\sqrt{2}}$

→ Taking the value of √2 as 1.41:

$\sf{=6\times1.41}$

$\sf{=8.46}$

Perimeter of a square = 4a

= 4 x 8.46

= 33.84 cm

★ Final Answers:

Area of the square = 72 cm²

Perimeter of the square = 33.84 cm

Answer 2

Answer:

• A square have all the sides equal
• A square have all the sides equalThe measure of all interior angles in square is 90⁰
• Diagonals of square makes right angle triangle

Let a be the side length of the square

if the diagonals of the square is 5root 2cm

Then by Pythagoras theorem

we have

${a}^{2} + {a}^{2} = (5 \sqrt{2} ) {}^{2} \\ 2a {}^{2} =50\\ {a}^{2} = 25 \\ a = 5cm$

Thus the side of square is 5cm

perimeter of a square=4xside

=4x5=20cm

Area of square=side²

=5²=25sqcm

Hence perimeter of a square=20cm and area is 25cm²

Step-by-step explanation:

=>area of square=1/2(d)²

=>1/2x12x12

=>6x12=72

$side \: of \: square = \sqrt{area} \\ = \sqrt{72} = \sqrt{2 \times 2 \times 2 \times 3 \times 3} \\ =2 \times 3 \sqrt{2} = 6 \times 1.41 \\ = 8.46cm$

=>Perimeter of a square=4xside

=>4x8.46

=>33.84cm