Hiro bought a small carton of milk at lunch.

A rectangular prism with length of 3 inches, width of 3 inches, and height of 6.5 inches. A triangular prism. The triangular side has a base of 3 inches and height of 1.5 inches. The prism has a height of 3 inches.

If the approximate dimensions of the milk carton are shown, what is the minimum amount of cardboard needed to make the milk carton? Round to the nearest whole number.
65 inches squared
95 inches squared
104 inches squared
119 inches squared

Answer

If I understand the problem correctly, It would be 95 inches squared although the number I got was 95.74, which would actually round to 96. What I think it is asking for is the surface area of the milk carton.

Bottom:

length * width

3 * 3 = 9

Rectangular Sides:

One side would be the length or width (which both equal 3) times the height (6.5), and there are 4 total sides.

number of sides(length or width * height)

4(3 * 6.5) = 4(19.5) = 78

Triangular Sides:

One side would be * base (3) times height (1.5), and there are 2 triangular sides.

2(1/2(base * height))

2(1/2(3 * 1.5)) = 3 * 1.5 (The 2 and the 1/2 cancel each other out) = 4.5

The Roof-shaped Top Surfaces:

These are rectangles that you the width is equal to the length of the rectangular prism, and the length is equal to the one side of the triangle. You can find that length by using the Pythagorean theorem () which 1.5 is half of the base and the other 1.5 is the height. There are 2 of these rectangles making the final equation ≈ 4.24.

Now, add up each of the values:

9 + 78 + 4.5 + 4.24 = 95.74.

Comment if you see an error in my work.