Find the surface area of the box shown. $\newline$ S.A. $=$ $\square$ in. $^{2}$

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Q. Find the surface area of the box shown.

\newline

S.A.

=

\square

in.

^{2}

Identify dimensions: Identify the dimensions of the box. Let's say the length is $l$ inches, the width is $w$ inches, and the height is $h$ inches.
Calculate one side area: Calculate the area of one side $length \times width$ . This is one of the faces of the box. $\text{Area} = l \times w$
Calculate total length $\times$ width area: Since a box has two of each type of face, multiply the area of one face by $2$ to get the total area for those faces. $\newline$ Total area for length $\times$ width faces = $2 \times (l \times w)$
Calculate second face area: Calculate the area of the second type of face (width $\times$ height). $\newline$ Area = $w \times h$
Calculate total width $x$ height area: Multiply the area of the second type of face by $2$ . $\newline$ Total area for width $x$ height faces = $2 \times (w \times h)$
Calculate third face area: Calculate the area of the third type of face $length \times height$ . $\text{Area} = l \times h$
Calculate total length $x$ height area: Multiply the area of the third type of face by $2$ . $\newline$ Total area for length $x$ height faces = $2 \times (l \times h)$
Calculate total surface area: Add up the total areas of all the faces to get the surface area of the box. $S.A. = 2 \times (l \times w) + 2 \times (w \times h) + 2 \times (l \times h)$
Plug in actual dimensions: Plug in the actual dimensions of the box into the formula. Let's say $l = 5$ in, $w = 3$ in, and $h = 4$ in. $\text{S.A.} = 2 \times (5 \times 3) + 2 \times (3 \times 4) + 2 \times (5 \times 4)$
Perform calculations: Perform the calculations. $\newline$ S.A. = $2 \times 15 + 2 \times 12 + 2 \times 20$ $\newline$ S.A. = $30 + 24 + 40$
Add values for final area: Add up the values to get the final surface area. $\newline$ $S.A. = 30 + 24 + 40$ $\newline$ $S.A. = 94$ in $^2$