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A. Lucy needs to decide between two tables for the conference room. One is rectangular, 5 feet wide by 9 feet long. The other is a circle 8 feet in diameter.

1.) To the nearest tenth, the circumference of the circular table is ____?

2.) To the nearest tenth, the perimeter of the rectangular table is ____?

3.) Which table would seat more people?


b. A parallelogram has area of 234 cm^2. What is the measure of the height if the base is 12 cm?

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Answer:

Explanation:

The circumference of the circular table can be found using the formula:

circumference = π × diameter

The diameter of the circle is 8 feet, so:

circumference = π × 8 feet

circumference ≈ 25.1 feet (rounded to the nearest tenth)

Answer: Approximately 25.1 feet.

The perimeter of the rectangular table is the sum of the lengths of all four sides. Since the table is 5 feet wide and 9 feet long, the perimeter is:

perimeter = 2(5 feet) + 2(9 feet)

perimeter = 10 feet + 18 feet

perimeter = 28 feet

Answer: 28 feet.

To determine which table would seat more people, we need to compare their areas. The area of the rectangular table is:

area = length × width

area = 9 feet × 5 feet

area = 45 square feet

The area of the circular table is:

area = π × (radius)^2

area = π × (4 feet)^2

area ≈ 50.3 square feet (rounded to the nearest tenth)

Therefore, the circular table has a larger area and would seat more people.

Answer: The circular table would seat more people.

B.

The area of a parallelogram can be found using the formula:

area = base × height

We are given that the base is 12 cm and the area is 234 cm^2. Substituting these values into the formula, we get:

234 cm^2 = 12 cm × height

Solving for the height, we divide both sides by 12 cm:

height = 234 cm^2 / 12 cm

height ≈ 19.5 cm (rounded to the nearest tenth)

Answer: The height of the parallelogram is approximately 19.5 cm.

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