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A rectangular invitation card measuring 120 mm by 15 cm has a circular photo with a diameter of 80 mm printed on it. Calculate: (a) The area of the invitation card. (b) The area of the invitation card

Mathematics

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Answers

2 parts
a

18000 mm2\text{18000 mm}^2

b

12976 mm2\text{12976 mm}^2

Step-by-step solution

5 steps

Here are the solutions to the questions:

Part a· 2 steps

  1. Identify the dimensions of the rectangular invitation card and convert units to millimeters.

    The width of the card is 120 mm120 \text{ mm}.
    The length of the card is 15 cm15 \text{ cm}.
    To convert centimeters to millimeters, multiply by 10:

    15 cm=15×10 mm=150 mm15 \text{ cm} = 15 \times 10 \text{ mm} = 150 \text{ mm}
  2. Calculate the area of the rectangular invitation card using the formula Area = length ×\times width.

    Area of rectangle=150 mm×120 mm\text{Area of rectangle} = 150 \text{ mm} \times 120 \text{ mm} Area of rectangle=18000 mm2\text{Area of rectangle} = 18000 \text{ mm}^2

    The area of the rectangular invitation card is 18000 mm2\boxed{\text{18000 mm}^2}.

Part b

12976 mm2\text{12976 mm}^2

  1. Calculate the radius of the circular photo.

    The diameter of the circular photo is 80 mm80 \text{ mm}.
    The radius is half of the diameter:

    Radius=80 mm2=40 mm\text{Radius} = \frac{80 \text{ mm}}{2} = 40 \text{ mm}
  2. Calculate the area of the circular photo using the formula Area = π×radius2\pi \times \text{radius}^2, with π=3.14\pi = 3.14.

    Area of circle=3.14×(40 mm)2\text{Area of circle} = 3.14 \times (40 \text{ mm})^2 Area of circle=3.14×1600 mm2\text{Area of circle} = 3.14 \times 1600 \text{ mm}^2 Area of circle=5024 mm2\text{Area of circle} = 5024 \text{ mm}^2
  3. Calculate the area of the rectangular invitation card without the photo by subtracting the area of the circle from the total area of the rectangle (calculated in part a).

    Area without photo=Area of rectangle−Area of circle\text{Area without photo} = \text{Area of rectangle} - \text{Area of circle} Area without photo=18000 mm2−5024 mm2\text{Area without photo} = 18000 \text{ mm}^2 - 5024 \text{ mm}^2 Area without photo=12976 mm2\text{Area without photo} = 12976 \text{ mm}^2

    The area of the rectangular invitation card without the photo is 12976 mm2\boxed{\text{12976 mm}^2}.

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