NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - True or False Questions
Question 15

Question. 15

Area of a square is doubled if the side of the square is doubled.

Answer:

false

Detailed Answer with Explanation:

Why the statement is false

  1. Let the side be (a).
    Original area = side × side = (a imes a).
    So, original area = (a^2).
  2. Now double the side.
    New side = (2a).
  3. Find the new area.
    New area = new side × new side = ((2a) imes (2a)).
    = (2 imes 2 imes a imes a).
    = (4 imes a^2).
    So, new area = (4a^2).
  4. Compare the areas.
    Original area = (a^2).
    New area = (4a^2).
    Therefore, new area = (4 imes) the original area (four times), not double.

Quick number check:
If (a = 5) cm, original area = (5 imes 5 = 25 ext{cm}^2).
New side = (10) cm, new area = (10 imes 10 = 100 ext{cm}^2).
(100 = 4 imes 25), so the area becomes four times.

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