Acandy bar box is in the shape of a triangular prism. the volume of the box is 2,400 cubic centimeters. a triangular prism is shown with base of triangle labeled 16 cm, sides of triangles labeled 17 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)

  A) 15 cm

  B) 1240 cm²

Step-by-step explanation:

Part A: The height of the triangular base can be found a couple of ways. One is to use the Pythagorean theorem.

The triangular base is isosceles, so the height, half its base (8 cm) and the long edge (17 cm) form a right triangle. The height is then found from ...

  17² = 8² + height²

  289 -64 = height² . . . . . subtract 64

  √225 = 15 = height . . . . take the square root

The height of the triangular base is 15 cm.

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Part B: The volume of a prism is given by ...

  V = Bh

where B is the area of the base and h is the length ("heigh") of the prism. We can use this formula to find B, the area of each of the triangular bases of the prism.

  2400 cm³ = B·(20 cm)

  2400 cm³/(20 cm) = B = 120 cm² . . . . . area of one end of the prism

Now the lateral area of the prism is the product of its length (20 cm) and the perimeter of its base (17 cm + 17 cm + 16 cm). That area is ...

  lateral area = (20 cm)(50 cm) = 1000 cm²

Together with the areas of the two ends, we find the total area of the cardboard box to be ...

  total area = lateral area + 2×base area = 1000 cm² + 2×120 cm²

  total area = 1240 cm²

Note that you can also find the height of the base triangle from the base area.

  A = (1/2)bh

  120 cm² = (1/2)(16 cm)h

  120 cm²/(8 cm) = h = 15 cm

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

i think it would be 42cm