To find out how much red foil is needed for the sides of the triangular prism (i.e., the lateral surface area), we need to determine the area of the triangular faces and the rectangular lateral faces.
Step 1: Calculate the area of the triangular faces
The triangular faces are not explicitly stated which specific dimension represents the base, but since it mentions that one side of the triangle is 10 cm and the height is given as 6 cm, we'll use them directly in the area formula for the triangle.
The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Assuming that the base of the triangle is 10 cm and the height is 6 cm:
\[ \text{Area of one triangular face} = \frac{1}{2} \times 10 , \text{cm} \times 6 , \text{cm} = 30 , \text{cm}^2 \]
Since there are two triangular faces (top and bottom), we multiply by 2:
\[ \text{Total area of triangular faces} = 2 \times 30 , \text{cm}^2 = 60 , \text{cm}^2 \]
Step 2: Calculate the area of the rectangular lateral faces
The prism has three rectangular faces. The widths are given as follows:
- The base of the rectangle is the height of the prism, which is 16 cm, and the height of the rectangular face corresponds to the side of the triangle (that forms the base of the prism).
The rectangles' widths correspond to different sides:
- The side opposite to the triangle heights (height = 6 cm, base = 10 cm) - one rectangle
- The other side (height = 6 cm, base = 10 cm) - another rectangle
- Lastly, the connecting rectangles which takes the height of the prism as 16 cm and the width as 20 cm.
Calculating the area of each rectangle:
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For the lateral sides, the area of one rectangle connected to the triangles:
\[ \text{Area} = \text{height} \times \text{length} = 16 , \text{cm} \times 6 , \text{cm} = 96 , \text{cm}^2 \]
And since there are 3 rectangles of that dimension:
\[ \text{Total area for 3 rectangles} = 3 \times 96 , \text{cm}^2 = 288 , \text{cm}^2 \]
Step 3: Calculate the total red foil needed for one candy bar
Now we add the surface area of the three rectangular lateral faces to that of the triangular faces:
\[ \text{Total red foil needed} = \text{Total area of triangular faces} + \text{Total area of rectangular sides} = 60 , \text{cm}^2 + 288 , \text{cm}^2 = 348 , \text{cm}^2 \]
Final Answer:
Thus, 348 cm² of red foil are needed for one candy bar.