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Chocolate Bliss makes a candy bar in the shape of a triangular prism . The prism is represented by the net given. For packaging the top and bottom are covered in gold foil and the faces are covered in red foil. How many cm squared of red foil are needed for one candy bar?

Measurements
The width of the top and bottom are 20 cm
the triangles connected to the sides are 6cm in length and 10 cm

1 answer

To calculate the amount of red foil needed for the faces of the triangular prism-shaped candy bar, we first need to determine the dimensions of the prism based on the information given.

  1. Identifying the Shape and Dimensions:

    • The prism has a triangular base.
    • The width (the base of the triangle) is 20 cm.
    • The height of the triangle is 6 cm.
    • The length of the prism (the length along the triangular prism) is 10 cm.

  2. Calculating the Area of the Triangle (Base): The area of the triangular base can be calculated using the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] where the base is 20 cm and the height is 6 cm: \[ \text{Area} = \frac{1}{2} \times 20 , \text{cm} \times 6 , \text{cm} = \frac{1}{2} \times 120 , \text{cm}^2 = 60 , \text{cm}^2 \]

  3. Calculating the Area of the Faces: The prism has two triangular bases (top and bottom), which are covered in gold foil (not counted in the red foil requirement), and three rectangular side faces.

    • Each triangular base area has been calculated as 60 cm².
    • Therefore, the top and bottom areas together do not contribute to the red foil.

    Now, let's calculate the area of the three rectangular faces that will be covered in red foil:

    • Each side face of the prism has a height equal to the length of the prism (10 cm) and a width equal to the base of the triangle (20 cm).

    The area of the first rectangular face is: \[ \text{Area}_{\text{rect1}} = \text{width} \times \text{length} = 20 , \text{cm} \times 10 , \text{cm} = 200 , \text{cm}^2 \]

    The second and third faces are identical to the first, as they also have the dimensions of width and length.

    Let's summarize:

    • \(\text{Area of all three rectangular faces} = \text{Area}{\text{rect1}} + \text{Area}{\text{rect2}} + \text{Area}_{\text{rect3}} = 200 , \text{cm}^2 + 200 , \text{cm}^2 + 200 , \text{cm}^2 = 600 , \text{cm}^2\)

  4. Total Red Foil Needed: Thus, the total area of red foil needed for one candy bar is: \[ \text{Total Red Foil Area} = 600 , \text{cm}^2 \]

Therefore, 600 cm² of red foil are needed for one candy bar.