Mathematics
snoopy007:

(05.05 HC) A candy bar box is in the shape of a triangular prism. The volume of the box is 3,240 cubic centimeters. A triangular prism is shown with base of triangle labeled 24 cm, sides of the triangle labeled 15 cm, and length of the box equal to 30 cm. Part A: What is the height of the base? Show your work. (5 points) Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)

AZ:

The volume of a triangular prism is equal to the area of the base (which is the triangle) times the length of the prism or another way to show that would be V = 1/2 * b * h * l where b is the base of the triangle h is the height of the triangle and l is the length of the triangular prism so the 1/2 * b * h is the area of the base (which is the triangle) and you multiply it by the length of the prism this image should help you visualize it

AZ:

so you're given the length of the prism and the base of the triangle and you also know the volume so V = 1/2 * b * h * l Volume = 3,240 b = 24 l = 30 plug in everything they told you and solve for 'h'

AZ:

For part B, the approximate amount of cardboard needed to make the box means we're looking for the surface area of the triangular prism So you have to find the area of each side of the prism and add it all up together remember that the area of the rectangles will be length * width and the area of triangles are 1/2 * base * height

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