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The diagram below shows a floor plan of a school ground. Use the diagram to answer the questions that follow:

Mathematics

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9 steps

2.1.1

  1. Identify the dimensions of the office from the diagram.

    The length of the office is 6 m6 \text{ m}.
    The breadth (height) of the office is the same as the height of the Strong Room, which is 3 m3 \text{ m}.

  2. Calculate the perimeter using the formula P=2(length+breadth)P = 2(\text{length} + \text{breadth}).

    P=2(6 m+3 m)P = 2(6 \text{ m} + 3 \text{ m}) P=2(9 m)P = 2(9 \text{ m}) P=18 mP = 18 \text{ m}

    The perimeter of the office is 18 m\boxed{\text{18 m}}.

    2.1.2

  3. Identify the dimensions of the office.

    Length (ll) = 6 m6 \text{ m}
    Breadth (bb) = 3 m3 \text{ m}

  4. Calculate the area using the formula A=length×breadthA = \text{length} \times \text{breadth}.

    A=6 m×3 mA = 6 \text{ m} \times 3 \text{ m} A=18 m2A = 18 \text{ m}^2

    The area of the office is 18 m2\boxed{\text{18 m}^2}.

    2.2.1

  5. Identify the dimensions of the playfield and ensure consistent units.

    The base of the playfield is 300 cm300 \text{ cm}. Convert this to meters:

    300 cm=300×1100 m=3 m300 \text{ cm} = 300 \times \frac{1}{100} \text{ m} = 3 \text{ m}

    The height of the playfield is 4 m4 \text{ m}.

  6. Calculate the area using the formula A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}.

    A=12×3 m×4 mA = \frac{1}{2} \times 3 \text{ m} \times 4 \text{ m} A=12×12 m2A = \frac{1}{2} \times 12 \text{ m}^2 A=6 m2A = 6 \text{ m}^2

    The area of the playfield is 6 m2\boxed{\text{6 m}^2}.

    2.2.2

  7. State the total area to be covered and the coverage per bag.

    Total area of playfield = 6 m26 \text{ m}^2
    Area covered by one bag of sand = 1.6 m21.6 \text{ m}^2

  8. Calculate the number of bags needed.

    Number of bags=Total areaArea covered by one bag\text{Number of bags} = \frac{\text{Total area}}{\text{Area covered by one bag}} Number of bags=6 m21.6 m2/bag\text{Number of bags} = \frac{6 \text{ m}^2}{1.6 \text{ m}^2/\text{bag}} Number of bags=3.75 bags\text{Number of bags} = 3.75 \text{ bags}
  9. Round up to the nearest whole number since you cannot buy a fraction of a bag.

    They will need to buy 4 bags\boxed{\text{4 bags}}.

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