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

Question 19

Why the statement is false:

1. What is perimeter? It is the total length around a shape.
   For a rectangle:
   ( P = 2 imes ( ext{length} + ext{height}) )
2. What is area? It is the amount of surface the wall covers (the whole face we paint).
   For a rectangle:
   ( A = ext{length} imes ext{height} )
3. Painting uses area, not perimeter.
   We pay for how much surface we cover with paint, so we need the area of the wall.
4. Quick example:
   ( ext{length} = 4, ext{m})
   ( ext{height} = 3, ext{m})
   
   Area:
   ( A = ext{length} imes ext{height} )
   ( A = 4 imes 3 )
   ( A = 12, ext{m}^2 )
   
   Perimeter (just the border):
   ( P = 2 imes ( ext{length} + ext{height}) )
   ( P = 2 imes (4 + 3) )
   ( P = 14, ext{m} )
5. Cost idea: If paint costs (₹50) per ( ext{m}^2), then:
   ( ext{Cost} = 12 imes 50 = ₹600).
   Using perimeter would give (14 imes 50), which is wrong (and the units don’t match).

Conclusion: To find the cost of painting a wall, we must find its area, not its perimeter.