NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Multiple Choice Questions
Question 4

Question.  4

Length and breadth of a rectangular sheet of paper are 20 cm and 10 cm, respectively. A rectangular piece 5 cm × 2 cm is cut from the sheet as shown in Fig. 6.6. Which statement is correct for the remaining sheet?

(A)

Perimeter remains same but area changes.

(B)

Area remains the same but perimeter changes.

(C)

Both area and perimeter are changing.

(D)

Both area and perimeter remain the same.

Detailed Answer with Explanation:

  1. Write the sizes.
    Big sheet: (20 ext{ cm} imes 10 ext{ cm})
    Cut-out piece: (5 ext{ cm} imes 2 ext{ cm})

  2. Find the area of the big sheet (before cutting).
    (A_{ ext{big}} = 20 imes 10)
    (A_{ ext{big}} = 200 ext{cm}^2)

  3. Find the area of the cut-out piece.
    (A_{ ext{cut}} = 5 imes 2)
    (A_{ ext{cut}} = 10 ext{cm}^2)

  4. Find the remaining area (after cutting).
    (A_{ ext{remain}} = A_{ ext{big}} - A_{ ext{cut}})
    (A_{ ext{remain}} = 200 - 10)
    (A_{ ext{remain}} = 190 ext{cm}^2)

    Area changed from (200 ext{cm}^2) to (190 ext{cm}^2). So, the area changes.

  5. Think about the perimeter.
    Perimeter is the total length of the boundary.

    Before cutting, the sheet is a rectangle, so
    (P_{ ext{big}} = 2(20 + 10) = 60 ext{cm}).

    After cutting a small rectangle from the sheet (as shown in Fig. 6.6), the boundary is no longer a simple rectangle. The cut creates extra edges (an inner “corner/notch”), so the boundary becomes longer than before.

    Therefore, the perimeter changes (it increases from the original (60 ext{cm})).

  6. Conclusion.
    Area decreases and perimeter changes. Hence, the correct option is C.

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NCERT Exemplar Solutions Class 6 – Mathematics – Unit 6: Mensuration – Multiple Choice Questions | Detailed Answers