A book id 10 x 18cm long and 2cm thick. It has a protective paper” jacket ” over the entire cover and folding 5cm under the front and back how much paper is needed for the “jacket”

To find the total amount of paper required for the protective jacket, let's break down the dimensions step by step:

1. **Front and back covers**:  
   Each cover of the book is \( 10 \, \text{cm} \times 18 \, \text{cm} \).  
   So, the area of one cover is:
   \[
   A_{\text{cover}} = 10 \times 18 = 180 \, \text{cm}^2
   \]
   Since there are two covers (front and back), the total area for the covers is:
   \[
   2 \times 180 = 360 \, \text{cm}^2
   \]

2. **Spine (thickness of the book)**:  
   The spine is \( 2 \, \text{cm} \times 18 \, \text{cm} \), so the area of the spine is:
   \[
   A_{\text{spine}} = 2 \times 18 = 36 \, \text{cm}^2
   \]

3. **Folding under the front and back covers**:  
   The jacket folds 5 cm under both the front and back covers. Each fold has dimensions \( 5 \, \text{cm} \times 18 \, \text{cm} \), so the area of one fold is:
   \[
   A_{\text{fold}} = 5 \times 18 = 90 \, \text{cm}^2
   \]
   Since there are two folds (front and back), the total area for the folds is:
   \[
   2 \times 90 = 180 \, \text{cm}^2
   \]

4. **Total area of the jacket**:  
   The total area of the protective jacket is the sum of the areas of the front and back covers, the spine, and the two folds:
   \[
   A_{\text{total}} = 360 + 36 + 180 = 576 \, \text{cm}^2
   \]

So, the total amount of paper needed for the jacket is **576 cm²**.

Would you like further explanation or have any other questions?

Here are 5 related questions to expand this:
1. What if the folds were 6 cm instead of 5 cm? How much paper would be required?
2. If the book’s dimensions changed to 12 x 20 cm, how much paper would be needed?
3. How would the amount of paper change if the thickness was 3 cm?
4. What if the jacket also had an extra 2 cm overlap on the top and bottom edges?
5. Can you calculate the total surface area of the book without the jacket?

**Tip:** When solving real-world measurement problems, break the object down into smaller parts to calculate areas efficiently!

A book is 10 x 18 cm long and 2 cm thick. It has a protective paper jacket over the entire cover, folding 5 cm under the front and back. How much paper is needed for the jacket?

Learn how to calculate the total paper needed for a book jacket with dimensions 10x18 cm and 2 cm thickness. This problem covers key geometry concepts and step-by-step area calculations, suitable for students in Grades 6-8.

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