NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Problems and Solutions
Question 57

Question. 57

Area of each square on chess board = 4 sq cm. Find total area.

  • (a) Area left unoccupied.
  • (b) Area occupied.

Answer:

Total = 256 cm²
(a) 192 cm²
(b) 64 cm²

Detailed Answer with Explanation:

  1. Understand the board:

    A chessboard has 8 rows and 8 columns.

    Number of squares = \(8 \times 8\)

    \(8 \times 8 = 64\) squares

  2. Area of one square:

    Given: area of each square = \(4\,\text{cm}^2\)

  3. Total area of the chessboard:

    Total area = (number of squares) \(\times\) (area of one square)

    \(64 \times 4\)

    \(= 256\,\text{cm}^2\)

  4. Area occupied by pieces:

    (As used here) number of pieces on the board = \(16\)

    Each piece covers exactly one square \(\Rightarrow\) area covered by one piece = area of one square

    Occupied area = \(16 \times 4\)

    \(= 64\,\text{cm}^2\)

  5. Area left unoccupied:

    Unoccupied area = (total area) \(-\) (occupied area)

    \(256 - 64\)

    \(= 192\,\text{cm}^2\)

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 6: Mensuration – Problems and Solutions | Detailed Answers