Use the image to answer the question.
An illustration shows an unfolded version of a triangular prism.
There are 3 horizontal rectangles stacked on top of one another. The first and the last are similar and the middle one is larger. The horizontal length of the three rectangles is 20 centimeters. The vertical width of the second rectangle is 16 centimeters. There are two similar triangles adjoined to the left and right of the second rectangle, with the rectangle width as the triangle bases. The perpendicular length of the triangle, drawn as a dotted line from the top vertex to the middle of the base, is 6 centimeters; it is denoted by a right angle symbol. The length of the hypotenuse slant is 10 centimeters. All interior lines are drawn as dashed lines, and all outer lines are solid.
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 cm2 of red foil are needed for one candy bar?
To calculate the total surface area of the triangular prism, we need to find the area of each individual face and then add them up.
First, let's calculate the area of the three rectangles:
Rectangle 1 and 3: 20 cm (horizontal length) x 16 cm (vertical width) = 320 cm2 each
Rectangle 2: 20 cm (horizontal length) x 16 cm (vertical width) = 320 cm2
Now, let's calculate the area of the two triangles:
Triangle 1 and 3: (1/2) x 16 cm (base) x 6 cm (height) = 48 cm2 each
Triangle 2: (1/2) x 16 cm (base) x 10 cm (hypotenuse) = 80 cm2 (Since this triangle is bigger)
Now, let's add up all the areas and multiply by 2 for the two faces of the prism:
Total area = (320 cm2 + 320 cm2 + 320 cm2 + 48 cm2 + 48 cm2 + 80 cm2) x 2 = (1136) x 2 = 2272 cm2
Therefore, 2272 cm2 of red foil are needed for one candy bar.