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