Question: Betty has the option of using three types of tables in her coffee shop:
• square tables with a side length of 36 inches
• rectangular tables 20 inches wide and 73 inches long
• round (circular) tables with a diameter of 42 inches.
Which type of table has the largest area?
1. **State the problem:** We need to find which table type has the largest area among square, rectangular, and circular tables.
2. **Formulas for area:**
- Square area: $$A = s^2$$ where $s$ is the side length.
- Rectangle area: $$A = w \times l$$ where $w$ is width and $l$ is length.
- Circle area: $$A = \pi r^2$$ where $r$ is the radius.
3. **Calculate each area:**
- Square: side length $s = 36$ inches
$$A = 36^2 = 1296$$ square inches.
- Rectangle: width $w = 20$ inches, length $l = 73$ inches
$$A = 20 \times 73 = 1460$$ square inches.
- Circle: diameter $d = 42$ inches, radius $r = \frac{42}{2} = 21$ inches
$$A = \pi \times 21^2 = \pi \times 441 = 441\pi \approx 1385.44$$ square inches.
4. **Compare areas:**
- Square: $1296$ sq in
- Rectangle: $1460$ sq in
- Circle: $1385.44$ sq in
5. **Conclusion:** The rectangular table has the largest area of $1460$ square inches.