Answer :
Certainly! Let's go through this problem step-by-step to determine the total area if we use 5 smaller pieces from the first cardboard and 3 smaller pieces from the second cardboard.
### Step 1: Convert Mixed Numbers to Improper Fractions
1. The first cardboard:
- Length: \(2 \frac{1}{5}\) is \(2 + 0.2 = 2.2\)
- Breadth: \(1 \frac{1}{5}\) is \(1 + 0.2 = 1.2\)
2. The second cardboard:
- Length: \(3 \frac{1}{5}\) is \(3 + 0.2 = 3.2\)
- Breadth: \(2 \frac{2}{5}\) is \(2 + 0.4 = 2.4\)
### Step 2: Calculate the Areas of the Cardboards
1. Area of the first cardboard:
[tex]\[ \text{Area}_{\text{first}} = \text{Length}_{\text{first}} \times \text{Breadth}_{\text{first}} = 2.2 \times 1.2 = 2.64 \, \text{m}^2 \][/tex]
2. Area of the second cardboard:
[tex]\[ \text{Area}_{\text{second}} = \text{Length}_{\text{second}} \times \text{Breadth}_{\text{second}} = 3.2 \times 2.4 = 7.68 \, \text{m}^2 \][/tex]
### Step 3: Calculate the Area of One Small Piece from Each Cardboard
Since each cardboard is divided into 10 equal pieces:
1. Area of one small piece from the first cardboard:
[tex]\[ \text{Area}_{\text{piece, first}} = \frac{\text{Area}_{\text{first}}}{10} = \frac{2.64}{10} = 0.264 \, \text{m}^2 \][/tex]
2. Area of one small piece from the second cardboard:
[tex]\[ \text{Area}_{\text{piece, second}} = \frac{\text{Area}_{\text{second}}}{10} = \frac{7.68}{10} = 0.768 \, \text{m}^2 \][/tex]
### Step 4: Calculate the Total Area Used
Using 5 small pieces from the first cardboard and 3 small pieces from the second cardboard:
1. Area from 5 pieces from the first cardboard:
[tex]\[ \text{Total Area}_{\text{from first}} = 5 \times \text{Area}_{\text{piece, first}} = 5 \times 0.264 = 1.32 \, \text{m}^2 \][/tex]
2. Area from 3 pieces from the second cardboard:
[tex]\[ \text{Total Area}_{\text{from second}} = 3 \times \text{Area}_{\text{piece, second}} = 3 \times 0.768 = 2.304 \, \text{m}^2 \][/tex]
3. Total area of the new cardboard:
[tex]\[ \text{Total Area} = \text{Total Area}_{\text{from first}} + \text{Total Area}_{\text{from second}} = 1.32 + 2.304 = 3.624 \, \text{m}^2 \][/tex]
### Conclusion
Therefore, the total area of a cardboard made using 5 small pieces from the first cardboard and 3 small pieces from the second cardboard is [tex]\(3.624 \, \text{m}^2\)[/tex].
### Step 1: Convert Mixed Numbers to Improper Fractions
1. The first cardboard:
- Length: \(2 \frac{1}{5}\) is \(2 + 0.2 = 2.2\)
- Breadth: \(1 \frac{1}{5}\) is \(1 + 0.2 = 1.2\)
2. The second cardboard:
- Length: \(3 \frac{1}{5}\) is \(3 + 0.2 = 3.2\)
- Breadth: \(2 \frac{2}{5}\) is \(2 + 0.4 = 2.4\)
### Step 2: Calculate the Areas of the Cardboards
1. Area of the first cardboard:
[tex]\[ \text{Area}_{\text{first}} = \text{Length}_{\text{first}} \times \text{Breadth}_{\text{first}} = 2.2 \times 1.2 = 2.64 \, \text{m}^2 \][/tex]
2. Area of the second cardboard:
[tex]\[ \text{Area}_{\text{second}} = \text{Length}_{\text{second}} \times \text{Breadth}_{\text{second}} = 3.2 \times 2.4 = 7.68 \, \text{m}^2 \][/tex]
### Step 3: Calculate the Area of One Small Piece from Each Cardboard
Since each cardboard is divided into 10 equal pieces:
1. Area of one small piece from the first cardboard:
[tex]\[ \text{Area}_{\text{piece, first}} = \frac{\text{Area}_{\text{first}}}{10} = \frac{2.64}{10} = 0.264 \, \text{m}^2 \][/tex]
2. Area of one small piece from the second cardboard:
[tex]\[ \text{Area}_{\text{piece, second}} = \frac{\text{Area}_{\text{second}}}{10} = \frac{7.68}{10} = 0.768 \, \text{m}^2 \][/tex]
### Step 4: Calculate the Total Area Used
Using 5 small pieces from the first cardboard and 3 small pieces from the second cardboard:
1. Area from 5 pieces from the first cardboard:
[tex]\[ \text{Total Area}_{\text{from first}} = 5 \times \text{Area}_{\text{piece, first}} = 5 \times 0.264 = 1.32 \, \text{m}^2 \][/tex]
2. Area from 3 pieces from the second cardboard:
[tex]\[ \text{Total Area}_{\text{from second}} = 3 \times \text{Area}_{\text{piece, second}} = 3 \times 0.768 = 2.304 \, \text{m}^2 \][/tex]
3. Total area of the new cardboard:
[tex]\[ \text{Total Area} = \text{Total Area}_{\text{from first}} + \text{Total Area}_{\text{from second}} = 1.32 + 2.304 = 3.624 \, \text{m}^2 \][/tex]
### Conclusion
Therefore, the total area of a cardboard made using 5 small pieces from the first cardboard and 3 small pieces from the second cardboard is [tex]\(3.624 \, \text{m}^2\)[/tex].
