## anonymous one year ago PLEASE HELP? 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 box? Show your work. (5 points) Part B: What is the approximate amount of cardboard used to make the sides of the candy box? Explain how you got your answer. (5 points)

1. anonymous

2. anonymous

@dan815

3. anonymous

@nincompoop

4. anonymous

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5. anonymous

@JA1

6. nincompoop

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7. anonymous

PART A ____ So if (a)^2 + (b)^2 = (c)^2 , and a=5, b=?, c=13 , it's suffice to say that: (5)^2 + (?)^2 = (13)^2 (5)^2 = 25 , (13)^2 = 169 (c)^2 - (a)^2 = (b)^2 169 - 25 = 144 So now that you know your *squared* height, take the square root of that number: √(144) = 12 -> your height is 12.

8. anonymous

PART B ____ I'm not sure how you were taught, so I'll show work for different methods to get the same answer. ____ Method 1: Solving for the lateral surface area of the triangular prism (not using volume) Note that for the triangular prism: **DON'T include the 2 triangular bases. DO include the 3 rectangular sides** *lateral surface area does not include the area of the bases* *lateral surface area just includes the lateral faces* formula: (a + b + c)(h) [a, b, c still using the values from PART A; h being your height from PART A] Plug them into the above formula: (10 + 13 + 13)(20) -> (10 + 26)(20) -> (36)(20) = 720 => Your lateral surface area is 720. (If you forget to exclude the area of the bases, you will get the surface area of 840) ___________________ Method 2: Solving for the lateral surface area of the triangular prism (using volume) Note that we will be using surface area, height, and volume to find the lateral area this time. formula: A - 2 (V/h) [A is the surface area; V is the given volume; h is the height from PART A] Before we can plug things into the above formula, we need to find the surface area. Since we have already found the lateral surface area (the area of the 3 rectangular sides), we just have to solve for the area of the bases (the area of the 2 triangles). (Area of a triangle = (1/2)b*h or (0.5)(b*h) -> one-half of the base times the height We can do this 2 ways: 1) Using our base value from PART A which is 5, and our height from PART A which is 12 1/2(5*12) -> 1/2(60) -> 30. Because we split that triangle in half in PART A, there are 4 triangles (2 in each base). So 30(4) = 120. 2) Using the whole base of the triangle which is 10, and the height from PART A which is 12 1/2(10*12) -> 1/2(120) -> 60. Since this time we used each whole base, instead of splitting them, there are only 2 triangles (1 per base). So 60(2) = 120. Both ways gave you the same answer of 120. Now add the lateral surface area and the area of the bases. 720 + 120 720 + 120 = 840. 840 is your surface area. With that, you can now plug things into the formula. A - 2 (V/h) -> 840 - 2 (1200/20) = 720 => Your lateral surface area is 720. ___________________ Both Method 1 & Method 2 get you a lateral surface area of 720. ___ The approx. amount of cardboard used for the sides (aka lateral faces[aka rectangular sides]) of the candy box is 720.

9. anonymous