With examples, explain how to calculate different paper formats and sizes.

1. A4 paper size: The A4 paper size is commonly used for printing documents and measures 210mm x 297mm. To calculate the area of an A4 paper, you can multiply the length by the width. In this case, the area of an A4 paper would be 210mm x 297mm = 62,370 square millimeters.

2. Letter paper size: The letter paper size is commonly used in North America and measures 8.5 inches x 11 inches. To calculate the area of a letter paper, you can multiply the length by the width. In this case, the area of a letter paper would be 8.5 inches x 11 inches = 93.5 square inches.

3. Legal paper size: The legal paper size is also commonly used in North America and measures 8.5 inches x 14 inches. To calculate the area of a legal paper, you can multiply the length by the width. In this case, the area of a legal paper would be 8.5 inches x 14 inches = 119 square inches.

4. Tabloid paper size: The tabloid paper size is larger than the letter and legal sizes and measures 11 inches x 17 inches. To calculate the area of a tabloid paper, you can multiply the length by the width. In this case, the area of a tabloid paper would be 11 inches x 17 inches = 187 square inches.

Calculating Paper Formats and Sizes

1. ISO 216 (International Standard Paper Sizes)

- The ISO 216 standard defines a series of paper sizes based on a base size of A0 (841mm x 1189mm).
- Each subsequent size in the series is half the area of the previous size.
- The aspect ratio of all ISO 216 sizes is 1:√2 (approximately 1:1.414).

Formula to Calculate ISO 216 Sizes:

```
Width = 1189mm - 2^(-n/4)
Height = 841mm - 2^(-n/4)
```

- Where n is the size number (0, 1, 2, 3, ...)

Examples:

- A0: 841mm x 1189mm
- A1: 594mm x 841mm (half of A0)
- A4: 210mm x 297mm (quarter of A0)

2. US Letter and Legal Sizes

- US Letter: 8.5in x 11in
- US Legal: 8.5in x 14in

Formula to Convert US Sizes to ISO 216 Sizes:

```
Width = (US Width in inches) - 25.4mm / inch
Height = (US Height in inches) - 25.4mm / inch
```

Examples:

- US Letter to A4: 8.5in x 11in = 215.9mm x 279.4mm (close to A4's 210mm x 297mm)
- US Legal to A4: 8.5in x 14in = 215.9mm x 355.6mm (larger than A4)

3. Custom Paper Sizes

- Custom paper sizes can be calculated using the following formula:

```
Width = (Custom Width in millimeters)
Height = (Custom Height in millimeters)
```

- Custom sizes should adhere to the aspect ratio of the desired ISO 216 paper size to ensure proper scaling when printing or displaying.