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Calculate the total area of all the rectangular sides of the chocolate pack.

Mathematics

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Answer

81.6 cm2\text{81.6 cm}^2

102 mm\text{102 mm}

Step-by-step solution

6 steps

1.1.1) Calculate the total area of all the rectangular sides of the chocolate pack.

  1. Identify the dimensions of the rectangular sides.

    The chocolate pack is a triangular prism. It has three rectangular sides.
    The length of the prism is 8 cm8 \text{ cm}.
    The sides of the triangular base are 4.2 cm4.2 \text{ cm}, 3 cm3 \text{ cm}, and 3 cm3 \text{ cm}.
    Each rectangular side will have a length of 8 cm8 \text{ cm} and a width corresponding to one of the triangle's sides.

  2. Calculate the area of each rectangular side.

    Area of the first rectangular side (length 8 cm8 \text{ cm}, width 4.2 cm4.2 \text{ cm}):

    Area1=8 cm×4.2 cm=33.6 cm2\text{Area}_1 = 8 \text{ cm} \times 4.2 \text{ cm} = 33.6 \text{ cm}^2

    Area of the second rectangular side (length 8 cm8 \text{ cm}, width 3 cm3 \text{ cm}):

    Area2=8 cm×3 cm=24 cm2\text{Area}_2 = 8 \text{ cm} \times 3 \text{ cm} = 24 \text{ cm}^2

    Area of the third rectangular side (length 8 cm8 \text{ cm}, width 3 cm3 \text{ cm}):

    Area3=8 cm×3 cm=24 cm2\text{Area}_3 = 8 \text{ cm} \times 3 \text{ cm} = 24 \text{ cm}^2
  3. Calculate the total area of all rectangular sides.

    Total Area=Area1+Area2+Area3\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 Total Area=33.6 cm2+24 cm2+24 cm2\text{Total Area} = 33.6 \text{ cm}^2 + 24 \text{ cm}^2 + 24 \text{ cm}^2 Total Area=81.6 cm2\text{Total Area} = 81.6 \text{ cm}^2

    The total area of all the rectangular sides is 81.6 cm2\boxed{\text{81.6 cm}^2}.

    1.1.2) Calculate the perimeter of one triangle in mm.

  4. Identify the side lengths of the triangle.

    The sides of the triangular base are 4.2 cm4.2 \text{ cm}, 3 cm3 \text{ cm}, and 3 cm3 \text{ cm}.

  5. Calculate the perimeter in cm.

    The perimeter is the sum of all side lengths.

    Perimeter=4.2 cm+3 cm+3 cm\text{Perimeter} = 4.2 \text{ cm} + 3 \text{ cm} + 3 \text{ cm} Perimeter=10.2 cm\text{Perimeter} = 10.2 \text{ cm}
  6. Convert the perimeter from cm to mm.

    Since 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}:

    Perimeter in mm=10.2 cm×10mmcm\text{Perimeter in mm} = 10.2 \text{ cm} \times 10 \frac{\text{mm}}{\text{cm}} Perimeter in mm=102 mm\text{Perimeter in mm} = 102 \text{ mm}

    The perimeter of one triangle is 102 mm\boxed{\text{102 mm}}.

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