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Calculate the area of each of the following shapes:

Mathematics

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4 parts
a

45 m245\, \text{m}^2

b

7.5 cm27.5\, \text{cm}^2

c

39 m239\, \text{m}^2

d

12.4 cm212.4\, \text{cm}^2

Step-by-step solution

12 steps

Here are the areas of the shapes:

Part a· 3 steps

This is a rectangle.

  1. Identify the formula for the area of a rectangle.

    Area=length×width\text{Area} = \text{length} \times \text{width}
  2. Substitute the given values.

    Area=9 m×5 m\text{Area} = 9\, \text{m} \times 5\, \text{m}
  3. Calculate the area.

    Area=45 m2\text{Area} = 45\, \text{m}^2

    The area of shape (a) is 45 m2\boxed{45\, \text{m}^2}.

Part b

7.5 cm27.5\, \text{cm}^2

This is a triangle.

  1. Identify the formula for the area of a triangle.

    Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
  2. Substitute the given values.

    Area=12×5 cm×3 cm\text{Area} = \frac{1}{2} \times 5\, \text{cm} \times 3\, \text{cm}
  3. Calculate the area.

    Area=12×15 cm2\text{Area} = \frac{1}{2} \times 15\, \text{cm}^2 Area=7.5 cm2\text{Area} = 7.5\, \text{cm}^2

    The area of shape (b) is 7.5 cm2\boxed{7.5\, \text{cm}^2}.

Part c

39 m239\, \text{m}^2

This is a parallelogram.

  1. Identify the formula for the area of a parallelogram.

    Area=base×height\text{Area} = \text{base} \times \text{height}
  2. Substitute the given values.

    Area=6 m×6.5 m\text{Area} = 6\, \text{m} \times 6.5\, \text{m}
  3. Calculate the area.

    Area=39 m2\text{Area} = 39\, \text{m}^2

    The area of shape (c) is 39 m2\boxed{39\, \text{m}^2}.

Part d

12.4 cm212.4\, \text{cm}^2

This is a right-angled triangle.

  1. Identify the formula for the area of a triangle.

    Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
  2. Substitute the given values.

    Area=12×4 cm×6.2 cm\text{Area} = \frac{1}{2} \times 4\, \text{cm} \times 6.2\, \text{cm}
  3. Calculate the area.

    Area=12×24.8 cm2\text{Area} = \frac{1}{2} \times 24.8\, \text{cm}^2 Area=12.4 cm2\text{Area} = 12.4\, \text{cm}^2

    The area of shape (d) is 12.4 cm2\boxed{12.4\, \text{cm}^2}.

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