Certainly! Let's find the total surface area of a book that is 22 cm long, 14.5 cm wide, and 4 cm high. We need to consider each face of the book and how many times each face appears.
### Step-by-Step Solution:
1. Identify the dimensions of the book:
- Length (L) = 22 cm
- Width (W) = 14.5 cm
- Height (H) = 4 cm
2. Calculate the area of each face:
- There are three distinct faces to consider:
- The front and back faces (Length x Width)
- The top and bottom faces (Length x Height)
- The left and right faces (Width x Height)
3. Compute the area for each face:
- Front and Back Faces:
[tex]\[
\text{Area}_{\text{Front/Back}} = \text{Length} \times \text{Width} = 22 \, \text{cm} \times 14.5 \, \text{cm} = 319 \, \text{cm}^2
\][/tex]
- Top and Bottom Faces:
[tex]\[
\text{Area}_{\text{Top/Bottom}} = \text{Length} \times \text{Height} = 22 \, \text{cm} \times 4 \, \text{cm} = 88 \, \text{cm}^2
\][/tex]
- Left and Right Faces:
[tex]\[
\text{Area}_{\text{Left/Right}} = \text{Width} \times \text{Height} = 14.5 \, \text{cm} \times 4 \, \text{cm} = 58 \, \text{cm}^2
\][/tex]
4. Calculate the number of each face:
- Since the book is a rectangular prism, each face appears twice.
5. Calculate the total surface area:
- Each of the three types of faces appears twice, so we multiply each calculated area by 2 and then sum them up:
[tex]\[
\text{Total Surface Area} = 2 \times (319 \, \text{cm}^2 + 88 \, \text{cm}^2 + 58 \, \text{cm}^2)
\][/tex]
- Performing the addition inside the parenthesis:
[tex]\[
\text{Total Surface Area} = 2 \times (319 + 88 + 58) \, \text{cm}^2
\][/tex]
[tex]\[
\text{Total Surface Area} = 2 \times 465 \, \text{cm}^2
\][/tex]
[tex]\[
\text{Total Surface Area} = 930 \, \text{cm}^2
\][/tex]
### Answer:
The total surface area of the book is [tex]\( 930 \, \text{cm}^2 \)[/tex].
