A circular dance stage nas a perimeter of 28pi feet . What is the area in square feet of this dance stage?

Answer 1

You can use the perimeter or circumference to determine the diameter of the stage first. Then you can use this diameter to calculate the area of the stage.

The perimeter or circumference (C) of a circle can be calculated using the following, where d is the diameter of the stage:

C = ¶ • d

Here C= 28 ¶, so we can substitute this expression for C and solve for d:

28• ¶ = ¶• d

If you divide both sides of the equation by ¶, the diameter (d) will be 28 feet and the radius will be half of the diameter or 14 feet.

r = 14 feet

Next calculate the area using: A = ¶ • r²

A = 3.14 • 14²

A = 3.14 • 196

A = 615.44 ft²

Answer 2

You can use the perimeter or circumference to determine the diameter of the stage first. Then you can use this diameter to calculate the area of the stage.

The perimeter or circumference (C) of a circle can be calculated using the following, where d is the diameter of the stage:

C = ¶ • d

Here C= 28 ¶, so we can substitute this expression for C and solve for d:

28• ¶ = ¶• d

If you divide both sides of the equation by ¶, the diameter (d) will be 28 feet and the radius will be half of the diameter or 14 feet.

r = 14 feet

Next calculate the area using: A = ¶ • r²

A = 3.14 • 14²

A = 3.14 • 196

A = 615.44 ft²

Answer 3

A = π(d/2)² = π[(C/π)/2]²

Plug in the value of C (the perimeter) and finish from here.