Question

How can you calculate the area of the circle if you know the circle’s circumference? Show all work to support your thinking.

Answer 1

Answer:

  A = (1/2)Cr . . . or . . . A = C^2/(4π)

Step-by-step explanation:

The diagram shows the area of the circle being redrawn as a parallelogram with the length of it being half the circumference and the height of it being the radius of the circle.

The area of the parallelogram is the product of its length (C/2) and its height (r), so you can compute ...

  A = (1/2)Cr

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Given only the circumference, C = 2πr, you can find the value of r by dividing by its coefficient:

  C/(2π) = r

Using this in the above formula, the area can be found from the circumference only as ...

  A = (1/2)C·(C/(2π))

  A = C^2/(4π)