Question

A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.

A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 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)

Answer 1

Answer:

Step-by-step explanation:

Part A:

In the purple writing, I found the height of the triangle using the Pythagorean theorem.

I think this is what the question is calling the "height of the box".

height of the box = 15 cm

Part B:

The amount of cardboard needed for the sides will be the lateral area of this prism.

lateral area = perimeter of triangle * height of prism

lateral area = (16 + 17 + 17) * 20

lateral area = 50 * 20

lateral area = 1,000 cm2

Answer 2

Answer:

  Height of the base = 10cm

  Amount of cardboard used to make the candy box = 820cm²

Step-by-step explanation:

Given a candy box is in the shape of triangular prism.

            Volume of the box = 1200 cm³

            Base of the triangle = 10cm

            Side of the triangle = 13cm

            Length of the box = 20 cm

             Let the height of the base = h cm

Part A:

We know,

Volume of the triangular prism = 1/2×(Base of triangle)×(Height of triangle)×(length of prism)

                                           1200 = (1/2)×10×h×20

                                           1200 = 100h

                                                 h = 1200/100

                                                 h = 12 cm  

         So, height of the triangle = 10cm

Part B:

      To find the approximate amount of cardboard used to make the candy box we need to find the total surface area of the triangular prism.

Total surface area of triangular prism = area of 2 congruent triangles + area of 2 side rectangles and 1 base rectangle

           Area of triangle = (1/2)×base×height

                                      = (1/2)×10×10

                                      = 50 cm²

Area of side rectangle = side length × breadth

                                      = 13×20

                                      = 260 cm²

Area of base rectangle = length × breadth

                                       =  20×10

                                       = 200 cm²

Total surface area of triangular prism = 2(50)+2(260)+200

                                                              = 100+520+200

                                                              = 820 cm²

  Total surface area of triangular prism = 820cm²

   Hence,

      Height of the base = 10cm

     Amount of cardboard used to make the candy box = 820cm²

     

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