Question

If the perimeter of a square is 40 cm, find (i) the length of a diagonal, and (ii) its area.
step by step please ​

Answer 1

Step-by-step explanation:

$perimeter = 40 \: cm \\ length \: of \: a \: diagonal \\ = {?} \\ area = {?} \\ perimeter = 4 \times side \\ 40 = 4 \times side \\ side = \frac{40}{4} \\ side = 10 \: cm \\ length \: of \: a \: diagonal = \sqrt{2 } \times side \\ = \sqrt{2 } \times 10 \\ 10 \sqrt{2} \: cm \\ area = (side) {}^{2} \\ = (10) {}^{2} \\ = 100 \: c {m}^{2}$

Answer 2

Answer :-

• The length of the diagonal of square = 10√2cm.
• The area of the square = 100cm².

Step-by-step explanation:

To Find :-

• The length of diagonal
• The area of Square

Solution:

Given that,

• Perimeter of square = 40cm

Therefore, the side of square is,

As we know that,

Perimeter of square = 4 × a,

Where,

• a = side of square

=> 4 × side = 40

=> side = 40/4

=> side = 10

Hence, The side of square is 10cm.

Now, According the question,

• The length of a diagonal of square

As we know that,

Diagonal of square = a√2,

Where,

• a = side of square

=> a√2

=> 10√2

Therefore, The diagonal of square is 10√2cm.

• The area of square

As we know that,

Area of square = (a)²,

Where,

• a = side of square

=> (a)²

=> (10)²

=> 100

Therefore, The area of square is 100cm².

Formula used :-

• Perimeter of square = 4 × a units
• Diagonal of square = a√2 units
• Area of square = (a)² sq. units.

Here,

• a = side of a square.