the circumference of a circle is 148ft. find its area

Answer 1

Recall the formula(s) of a circle:

Area = Pi * Radius²

Circumference = 2 * Pi * Radius

If Circumference is 148 ft, 148 = 2 * Pi * Radius

Therefore, 23.55 ft = Radius (rounded)

Plugged into the area formula,

Area = Pi * (23.55) ²

Area = 1,743.06 ft²

Note that Circumference is a measurement in ft, but Area is in ft².

Another tidbit is Pi itself. It is a Greek letter that comes from the Greek word for "Periphery" (aka Perimeter), being the letter "P" in Greek. This is because Pi represents the number of radii that fit halfway around the periphery/perimeter of a circle. Another name you might be more familiar with for the perimeter of a circle is "circumference". So the history of the name itself tells you what it is a measurement of!

Hope you found this helpful and have a good day Kymani.

-Michael

Answer 2

2*pi*R = 148

You could find from it the R = 148 / (2*pi) = 23.55

The Area is pi * R^2 = pi * 23.55^2 = 1742.34

Answer 3

That means that C = 148 ft is the circumference of this circle = 2πr, where r is the radius of the circle. We know that A = πr² is the area of the circle. By algebra, and the fact that 2πr = 148 ft, we know that r = (148/2π) ft, so A = πr² = π(148/2π)² ft² = (5476/π) ft²