Question

margo needs to wrap a gift for her sister. the gift is in the box shown below. image of a rectangular prism and its net with 36 in, 18 in, 18 in which of the following can be used to find the surface area, in square inches, of the box?
a. ( 2(18 \times 18) + 2(18 \times 36) )

b. ( 2(18 \times 18) + 4(18 \times 36) )

c. ( 4(18 \times 18) + 2(18 \times 36) )

d. ( 4(18 \times 18) + 4(18 \times 36) )

Explanation:

Step1: Identify the shape and dimensions

The box is a rectangular prism. From the net, we can see that there are two types of faces: square - like faces with side 18 in (but actually, looking at the net, the square - shaped faces (the ones with side 18 in) and the rectangular faces with dimensions 18 in and 36 in. Wait, actually, from the net, the number of faces: the two square - looking faces (but let's count the number of each type. Wait, the net has: looking at the diagram, the top and bottom are 18x18? No, wait, the length of the rectangular part is 36, and the other side is 18. Wait, actually, the rectangular prism has dimensions: let's see, the square - shaped faces (the ones with side 18) and the rectangular faces with length 36 and width 18. Wait, no, let's count the number of each face. In a rectangular prism, the surface area formula is \(2(lw + lh+wh)\). But from the net, we can see that there are 2 faces that are 18x18 (the top and bottom? Wait, no, looking at the net: the central part is a rectangle with length 36 and width 18, and then there are four rectangles attached? Wait, no, the net shows: the top square (18x18), then a central rectangle (36x18), then two side squares (18x18), then below the central rectangle, two more rectangles (18x36)? Wait, no, let's count the number of each type of face.

Wait, the net: the shape is a cross - like net for a rectangular prism. Let's see the dimensions. The square - shaped faces (with side 18) are 2? No, wait, looking at the net, there are 2 faces that are 18x18 (the top and bottom) and 4 faces that are 18x36 (the front, back, left, right). Wait, no, let's check the surface area formula for a rectangular prism. If the prism has length \(l = 36\), width \(w=18\), and height \(h = 18\). Then the surface area \(SA=2(lw + lh+wh)\). Substituting the values: \(lw=36\times18\), \(lh = 36\times18\), \(wh=18\times18\). So \(SA = 2(36\times18+36\times18 + 18\times18)=2(2\times(36\times18)+18\times18)=2\times18\times18+4\times18\times36\). Because \(2\times(2\times(36\times18))=4\times(36\times18)\) (wait, no: \(2(lw + lh+wh)=2(36\times18 + 36\times18+18\times18)=2\times18\times18+2\times36\times18+2\times36\times18=2(18\times18)+4(18\times36)\).

So the formula for the surface area is \(2(18\times18)+4(18\times36)\), which corresponds to option B.

Answer:

B. \(2(18\times 18)+4(18\times 36)\)