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Calculate the area of Fig 1.1.

Mathematics

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Answer

64 cm2\text{64 cm}^2

Step-by-step solution

4 steps
  1. Divide the L-shaped figure into two rectangles.

    We can divide Fig 1.1 into two rectangles:

    • Rectangle 1: The top-left vertical part.
    • Rectangle 2: The bottom-right horizontal part.
  2. Calculate the dimensions and area of Rectangle 1.

    Rectangle 1 has a width of 4 cm and a height of 6 cm.
    The area of Rectangle 1 (A1A_1) is:

    A1=width×height=4 cm×6 cm=24 cm2A_1 = \text{width} \times \text{height} = 4 \text{ cm} \times 6 \text{ cm} = 24 \text{ cm}^2
  3. Calculate the dimensions and area of Rectangle 2.

    Rectangle 2 has a height of 4 cm (given on the right side).
    The total width of the figure is the sum of the top horizontal segment (4 cm) and the inner horizontal segment (6 cm).
    Total width = 4 cm+6 cm=10 cm4 \text{ cm} + 6 \text{ cm} = 10 \text{ cm}.
    So, Rectangle 2 has a width of 10 cm and a height of 4 cm.
    The area of Rectangle 2 (A2A_2) is:

    A2=width×height=10 cm×4 cm=40 cm2A_2 = \text{width} \times \text{height} = 10 \text{ cm} \times 4 \text{ cm} = 40 \text{ cm}^2
  4. Calculate the total area of Fig 1.1.

    The total area (AtotalA_{\text{total}}) is the sum of the areas of Rectangle 1 and Rectangle 2.

    Atotal=A1+A2=24 cm2+40 cm2=64 cm2A_{\text{total}} = A_1 + A_2 = 24 \text{ cm}^2 + 40 \text{ cm}^2 = 64 \text{ cm}^2

    The area of Fig 1.1 is 64 cm2\boxed{\text{64 cm}^2}.

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