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The problem involves covering rectangular and circular tables with sheets of paper, and we need to calculate the area of paper required for each type of table. Here's how to approach it:

Part a

1. Rectangular Table: The dimensions of each rectangular table are given as 6 feet by 2 feet. The area $A$ of a rectangle is calculated as: $A = \text{length} \times \text{width}$ For the rectangular table: $A = 6 \, \text{ft} \times 2 \, \text{ft} = 12 \, \text{ft}^2$ So, the area of paper for each rectangular table is 12 ft².

2. Circular Table: The diameter of each circular table is given as 2.5 feet (2 feet 6 inches, which is 2.5 feet). The area $A$ of a circle is calculated as: $A = \pi r^2$ where $r$ is the radius (half of the diameter). So, the radius is: $r = \frac{2.5}{2} = 1.25 \, \text{ft}$ Now, calculating the area: $A = \pi (1.25)^2 = \pi \times 1.5625 \approx 4.91 \, \text{ft}^2$ The area of paper for each circular table is approximately 4.91 ft².

Part b

• There are 12 rectangular tables and 6 circular tables.
• The total area needed for the rectangular tables is: $12 \, \text{tables} \times 12 \, \text{ft}^2 = 144 \, \text{ft}^2$
• The total area needed for the circular tables is: $6 \, \text{tables} \times 4.91 \, \text{ft}^2 \approx 29.46 \, \text{ft}^2$
• Therefore, the total area for all the tables is: $144 \, \text{ft}^2 + 29.46 \, \text{ft}^2 = 173.46 \, \text{ft}^2$

Would you like a deeper breakdown of any part of this problem?

Related questions:

1. How do you calculate the area of a circle with different diameters?
2. How can you convert inches to feet in other measurements?
3. What is the total area needed if there were 20 circular tables instead of 6?
4. How do you handle calculations with fractions when converting measurements?
5. What would be the area needed if the dimensions of the rectangular tables changed to 8 feet by 3 feet?

Tip:

Always double-check units (feet, inches) to ensure accurate area calculations.