A candy 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.

  A: 15 cm

  B: 1120 cm²

Step-by-step explanation:

Part A: The triangle is isosceles, so its altitude bisects the base, giving two right triangles with hypotenuse 17 and leg 8. Then the other leg can be found from the Pythagorean theorem:

  h² +8² = 17²

  h = √(289 -65) = 15

The height of the base is 15 cm.

__

Part B: The total surface area of the prism is the sum of the lateral area and the areas of the triangular bases.

  Base area = (1/2)(b)(h) = (1/2)(8 cm)(15 cm) = 60 cm²

The lateral area is the product of the perimeter of the base and the length of the prism:

  LA = PL = (17 cm +17 cm +16 cm)(20 cm) = 1000 cm²

So, the total surface area of the box is ...

  2(base area) + lateral area = 2(60 cm²) +1000 cm² = 1120 cm²

The box uses about 1120 cm² of cardboard.

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.