Question

margo needs to wrap a gift for her sister. the gift is in the box shown below. 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 its dimensions

The box is a rectangular prism. From the net, we can see that the dimensions are \( l = 36 \) in, \( w = 18 \) in, and \( h = 18 \) in.

Step2: Recall the surface area formula for a rectangular prism

The surface area \( SA \) of a rectangular prism is given by \( SA = 2(lw + lh + wh) \).

Step3: Substitute the values into the formula

Substituting \( l = 36 \), \( w = 18 \), and \( h = 18 \) into the formula:
\[

$$\begin{align*} SA &= 2(36 \times 18 + 36 \times 18 + 18 \times 18)\\ &= 2(2 \times (36 \times 18) + (18 \times 18))\\ &= 4(36 \times 18) + 2(18 \times 18)\\ &= 2(18 \times 18) + 4(18 \times 36) \end{align*}$$

\]

Answer:

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