# Betty has the option of using three types of tables in her coffee shop: square tables with a side length of 42 inches; rectangular tables 26 inches wide and 73 2/3 inches long; and round tables with a diameter of 36 inches.

Which of the tables has the largest area? What is the area of that table?

## I don’t understand the steps here.

## To determine which table has the largest area, we need to calculate the area of each type of table and compare them.

1. Square Table:

The area of a square table is calculated by multiplying the length of one side by itself.

Side length = 42 inches

Area = 42 inches * 42 inches = 1,764 square inches

2. Rectangular Table:

The area of a rectangular table is calculated by multiplying the length by the width.

Length = 73 2/3 inches

Width = 26 inches

Area = 73 2/3 inches * 26 inches = 1,913.33 square inches

3. Round Table:

The area of a round table is calculated by using the formula A = πr^2, where π is a mathematical constant approximately equal to 3.14 and r is the radius (half of the diameter).

Diameter = 36 inches

Radius = 36 inches / 2 = 18 inches

Area = 3.14 * (18 inches)^2 = 1,018.48 square inches

Comparing the areas:

- Square Table: 1,764 square inches

- Rectangular Table: 1,913.33 square inches

- Round Table: 1,018.48 square inches

The rectangular table has the largest area, with an area of 1,913.33 square inches.

## To determine which table has the largest area, we need to compare the areas of each table.

Area of a square table:

The formula to find the area of a square is:

Area = side length * side length

Given that the side length of the square table is 42 inches:

Area = 42 inches * 42 inches

Area = 1764 square inches

Area of a rectangular table:

The formula to find the area of a rectangle is:

Area = length * width

Given that the length of the rectangular table is 73 2/3 inches and the width is 26 inches:

Area = 73 2/3 inches * 26 inches

To convert the mixed number to an improper fraction:

73 2/3 = (73 * 3 + 2) / 3 = 221/3

Area = (221/3) inches * 26 inches

To multiply fractions, just multiply the numerators and denominators:

Area = (221 * 26) / (3 * 1)

Area = 5734 square inches

Area of a round table:

The formula to find the area of a circle is:

Area = π * radius * radius

Given that the diameter of the round table is 36 inches, the radius is half the diameter:

Radius = 36 inches / 2

Radius = 18 inches

Using the approximation π = 3.14:

Area = 3.14 * 18 inches * 18 inches

Area = 1017.36 square inches (rounded to two decimal places)

Comparing the areas:

Square table area = 1764 square inches

Rectangular table area = 5734 square inches

Round table area = 1017.36 square inches

Based on the calculations, the rectangular table has the largest area, measuring 5734 square inches.

## A1 = 42 * 42

A2 = 26 * 221/3

A3 = 3.14159 * 18 * 18