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Calculate the area of a rectangle with side 4cm and 5cm. Your answer must be in cm. 2. Calculate the area of a square if its side is 3m. 3. Find the area of a square if the diameter is 30cm.

Mathematics

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1. Calculate the area of a rectangle with side 4cm and 5cm. Your answer must be in cm.

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

    The area of a rectangle is given by the formula:

    A=length×widthA = \text{length} \times \text{width}
  2. Substitute the given values into the formula.

    Given length =5 cm= 5 \text{ cm} and width =4 cm= 4 \text{ cm}.

    A=5 cm×4 cmA = 5 \text{ cm} \times 4 \text{ cm}
  3. Calculate the area.

    A=20 cm2A = 20 \text{ cm}^2

    The area of the rectangle is 20 cm2\boxed{\text{20 cm}^2}.

    2. Calculate the area of a square if its side is 3m.

  4. Identify the formula for the area of a square.

    The area of a square is given by the formula:

    A=side×side=side2A = \text{side} \times \text{side} = \text{side}^2
  5. Substitute the given value into the formula.

    Given side =3 m= 3 \text{ m}.

    A=(3 m)2A = (3 \text{ m})^2
  6. Calculate the area.

    A=9 m2A = 9 \text{ m}^2

    The area of the square is 9 m2\boxed{\text{9 m}^2}.

    3. Find the area of a square if the diameter is 30cm. π=3.14\pi = 3.14

    Assumption: The question likely intended to ask for the area of a circle given the diameter and the value of π\pi. A square does not have a diameter in the same way a circle does. If it were a square, π\pi would not be used.

  7. Determine the radius of the circle.

    The radius rr is half of the diameter.

    r=diameter2=30 cm2=15 cmr = \frac{\text{diameter}}{2} = \frac{30 \text{ cm}}{2} = 15 \text{ cm}
  8. Identify the formula for the area of a circle.

    The area of a circle is given by the formula:

    A=πr2A = \pi r^2
  9. Substitute the given values into the formula.

    Given r=15 cmr = 15 \text{ cm} and π=3.14\pi = 3.14.

    A=3.14×(15 cm)2A = 3.14 \times (15 \text{ cm})^2 A=3.14×225 cm2A = 3.14 \times 225 \text{ cm}^2
  10. Calculate the area.

    A=706.5 cm2A = 706.5 \text{ cm}^2

    The area of the circle is 706.5 cm2\boxed{\text{706.5 cm}^2}.

    4. Calculate the area of a triangle if the base is 28mm and the height is 15mm. Your answer should be in mm.

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

    The area of a triangle is given by the formula:

    A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}
  12. Substitute the given values into the formula.

    Given base =28 mm= 28 \text{ mm} and height =15 mm= 15 \text{ mm}.

    A=12×28 mm×15 mmA = \frac{1}{2} \times 28 \text{ mm} \times 15 \text{ mm}
  13. Calculate the area.

    A=14 mm×15 mmA = 14 \text{ mm} \times 15 \text{ mm} A=210 mm2A = 210 \text{ mm}^2

    The area of the triangle is 210 mm2\boxed{\text{210 mm}^2}.

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