Question

What is the area of a circle with circumference of 37.68? (Use 3.14 for p.)

Answer 1

the area of a circle is pi * r^2
circumference is 2 * pi * r

so we have to make the other side look like what area equals:
c = 2pr

divide both sides by 2

c/2 = p* r

square both sides and get
(c^2)/4 = p^2 * r^2

now divide both sides by pi and get
(c^2)/(4*pi) = pi * r^2

compare to area equation
pi * r^2 = a
pi * r^2 = (c^2)/(4*pi)

So
a = (c^2)/(4*pi)

So
a = (37.68^2)/(4 * 3.14)
a = 113.04