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Calculate the total area of three rectangular plots A, B, and C, given their dimensions and relationships in a diagram.

Mathematics

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Answer

3500 m23500 \text{ m}^2

Step-by-step solution

4 steps

To find the total area of the three plots A, B, and C, we need to calculate the area of each plot and then sum them up. All plots are rectangular, so their area is calculated as length ×\times width.

  1. Determine the dimensions and calculate the area of Plot A.

    From the diagram:

    • The length of Plot A is 40 m40 \text{ m}.
    • The total width of the farm is 50 m50 \text{ m} (indicated by the arrow at the bottom). Plot A spans this entire width.
    AreaA=length×width=40 m×50 m=2000 m2\text{Area}_A = \text{length} \times \text{width} = 40 \text{ m} \times 50 \text{ m} = 2000 \text{ m}^2
  2. Determine the dimensions and calculate the area of Plot B.

    From the diagram:

    • The length of Plot B is 30 m30 \text{ m}.
    • The total width of the bottom section (Plots B and C combined) is 50 m50 \text{ m}.
    • The width of Plot C is 20 m20 \text{ m}.
    • Therefore, the width of Plot B is 50 m−20 m=30 m50 \text{ m} - 20 \text{ m} = 30 \text{ m}.
    AreaB=length×width=30 m×30 m=900 m2\text{Area}_B = \text{length} \times \text{width} = 30 \text{ m} \times 30 \text{ m} = 900 \text{ m}^2
  3. Determine the dimensions and calculate the area of Plot C.

    From the diagram:

    • The length of Plot C is the same as the length of Plot B, which is 30 m30 \text{ m}.
    • The width of Plot C is 20 m20 \text{ m}.
    AreaC=length×width=30 m×20 m=600 m2\text{Area}_C = \text{length} \times \text{width} = 30 \text{ m} \times 20 \text{ m} = 600 \text{ m}^2
  4. Calculate the total area of the three plots.

    Total Area=AreaA+AreaB+AreaC\text{Total Area} = \text{Area}_A + \text{Area}_B + \text{Area}_C Total Area=2000 m2+900 m2+600 m2\text{Total Area} = 2000 \text{ m}^2 + 900 \text{ m}^2 + 600 \text{ m}^2 Total Area=3500 m2\text{Total Area} = 3500 \text{ m}^2

    The total area of the three plots A, B, and C is 3500 m23500 \text{ m}^2.

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