Hiro bought a small carton of milk at lunch. 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. A. 65 in2 B. 95in2 C. 104in2 D.119in2

Answer:[tex]C.\ 104\ in^2[/tex]Step-by-step explanation:At first, the question looks like an optimization problem, but since all the dimensions of the carton are given, we only have to compute the total area of the given figure. Let's calculate the front (and back) areas, which are rectangles [tex]A_1=(6.5)(3)=19.5\ in^2[/tex]Now with the lateral rectangles which happen to have the very same dimensions [tex]A_2=19.5\ in^2[/tex]Next, we compute the front and back triangles of base 3 in and height 1.5 in [tex]A_3=\frac{1}{2}(3)(1.5)=2.25\ in^2[/tex]Now, the lateral inclined rectangles of base 3 in and height 2 in [tex]A_4=(3)(2)=6\ in^2[/tex]Finally, the base rectangle who happens to be a square of side 3 in [tex]A_5=(3)(3)= 9\ in^2[/tex]This last area, unlike all others, is not doubled because its counterpart is inside the carton and is not part of the lateral area Our total area of cardboard is [tex]A_t=2(19.5)+2(19.5)+2(2.25)+2(6)+9=103.5\ in^2[/tex]The closest option to this answer is [tex]C.\ 104\ in^2[/tex]