Question

(c) If the perimeter of a square is 40 cm, find (i) the length of a diagonal, and (ii) its area.
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Answer 1

Required Answer :

• Length of the diagonal of square = 10√2 cm
• Area of the square = 100 cm²

Given :

• Perimeter of the square = 40 cm

To find :

• Length of the diagonal
• Area of the square

Solution :

In this question, we are given the perimeter of the square and we need to calculate the length of the diagonal and the area of square. And to calculate both of them we need the value of side of the square. So, firstly we will calculate the side of the square by using the formula of perimeter of square.

Using formula,

• Perimeter of square = 4 × side

Substituting the given values :

⇒ 40 = 4 × side

⇒ 40/4 = side

⇒ 10 = side

• Side of the square = 10 cm

Using formula,

• Length of the diagonal = √2 side

Substituting the given values :

⇒ Length of diagonal = √2 × 10

⇒ Length of diagonal = 10√2

• Length of the diagonal of square = 10√2 cm

Using formula,

• Area of square = (side)²

Substituting the given values :

⇒ Area of square = (10)²

⇒ Area of square = 100

• Area of the square = 100 cm²