Find the surface area of a textbook that is 2 in x 14 in x 9 in

1 answer

To find the surface area of a rectangular block (like a textbook) with dimensions 2 inches, 14 inches, and 9 inches, you can use the formula for the surface area \( S \) of a rectangular prism, which is:

\[ S = 2(ab + ac + bc) \]

where \( a \), \( b \), and \( c \) are the dimensions of the prism. In this case, let:

  • \( a = 2 \) inches
  • \( b = 14 \) inches
  • \( c = 9 \) inches

Plugging in the values:

\[ S = 2((2 \times 14) + (2 \times 9) + (14 \times 9)) \]

Calculating each term inside the parentheses:

  1. \( 2 \times 14 = 28 \)
  2. \( 2 \times 9 = 18 \)
  3. \( 14 \times 9 = 126 \)

Now, adding these results together:

\[ 28 + 18 + 126 = 172 \]

Now multiply by 2:

\[ S = 2 \times 172 = 344 \]

Thus, the surface area of the textbook is \( \boxed{344} \) square inches.