Let's work through this problem together:

Part a:

You are asked to find the area of paper that should be cut for each rectangular table.

• The dimensions of the rectangular table are given as 6 ft (length) by 2 ft (width).
• The area of a rectangle is calculated using the formula: $\text{Area} = \text{Length} \times \text{Width}$ Substituting the values: $\text{Area} = 6 \, \text{ft} \times 2 \, \text{ft} = 12 \, \text{ft}^2$ So, the area of paper for each rectangular table is 12 square feet.

For the circular table, the diameter is given as 2.6 ft.

• The area of a circle is calculated using the formula: $\text{Area} = \pi \times r^2$ where $r$ is the radius. Since the diameter is 2.6 ft, the radius $r$ is: $r = \frac{2.6}{2} = 1.3 \, \text{ft}$ Substituting the values into the area formula: $\text{Area} = \pi \times (1.3)^2 = \pi \times 1.69 \approx 5.31 \, \text{ft}^2$ So, the area of paper needed for each circular table is approximately 5.3 square feet (rounded to the nearest tenth).

Part b:

Now, there are 12 identical rectangular tables and 6 identical circular tables. You need to find the total area of paper needed for all the tables.

• Total area for rectangular tables: $\text{Total area for rectangular tables} = 12 \times 12 \, \text{ft}^2 = 144 \, \text{ft}^2$
• Total area for circular tables: $\text{Total area for circular tables} = 6 \times 5.31 \, \text{ft}^2 = 31.86 \, \text{ft}^2$
• Total area for all the tables: $\text{Total area} = 144 + 31.86 = 175.86 \, \text{ft}^2$ Rounded to the nearest tenth, the total area of paper needed is 175.9 square feet.

Would you like further details or have any questions?

Related Questions:

1. How would the area change if the dimensions of the rectangular table were doubled?
2. What would be the total area if there were 10 circular tables instead of 6?
3. How can you calculate the perimeter of the circular tables?
4. What is the total area of the classroom given its dimensions?
5. How many sheets of 1 ft² paper would be needed to cover all the tables?

Tip:

When calculating the area of circular shapes, always use the radius, which is half of the diameter, and ensure to round only at the final step for better accuracy.