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A rectangular stadium has a length of 20m and a width of 12m. It is surrounded by a uniform margin of 3m on all sides. Calculate the total area of the stadium including the margins and the area of the

Mathematics

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Answer

A=28 m,B=20 mA = 28 \text{ m}, B = 20 \text{ m}

320 m2320 \text{ m}^2

Step-by-step solution

5 steps

Here's the solution to your geometry problem:

1. Determine A and B

  1. Determine the total width, A.

    The total width A is the sum of the left margin, the width of the ground, and the right margin.

    A=3 m+20 m+5 mA = 3 \text{ m} + 20 \text{ m} + 5 \text{ m} A=28 mA = 28 \text{ m}
  2. Determine the total height, B.

    The total height B is the sum of the top margin, the height of the ground, and the bottom margin.

    B=3 m+12 m+5 mB = 3 \text{ m} + 12 \text{ m} + 5 \text{ m} B=20 mB = 20 \text{ m}

    The values for A and B are A=28 m,B=20 m\boxed{A = 28 \text{ m}, B = 20 \text{ m}}.

    2. Calculate the area that will be tilled
    Assuming "tilled" refers to the area of the stadium excluding the ground (e.g., for tiling stands or walkways).

  3. Calculate the area of the entire stadium.

    The area of the stadium is given by the formula Astadium=length×widthA_{stadium} = \text{length} \times \text{width}.

    Astadium=A×BA_{stadium} = A \times B Astadium=28 m×20 mA_{stadium} = 28 \text{ m} \times 20 \text{ m} Astadium=560 m2A_{stadium} = 560 \text{ m}^2
  4. Calculate the area of the ground.

    The area of the ground is given by the formula Aground=length×widthA_{ground} = \text{length} \times \text{width}.

    Aground=20 m×12 mA_{ground} = 20 \text{ m} \times 12 \text{ m} Aground=240 m2A_{ground} = 240 \text{ m}^2
  5. Calculate the area that will be tilled (tiled).

    This is the area of the stadium minus the area of the ground.

    Atilled=Astadium−AgroundA_{tilled} = A_{stadium} - A_{ground} Atilled=560 m2−240 m2A_{tilled} = 560 \text{ m}^2 - 240 \text{ m}^2 Atilled=320 m2A_{tilled} = 320 \text{ m}^2

    The area that will be tilled is 320 m2\boxed{320 \text{ m}^2}.

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