The circumference of a circle is given by
where C is the circumference and d is the length of the diameter.
We are told the circumference is 53.38 and to use 3.14 for pi. Substituting these into the equation above we get:
. Dividing 53.38 by 3.14 will give us the diameter which is approximately 18.5923.
The diameter is the distance from, a point on the circle through the center and to another point on the circle. It is twice the radius. So if we divide 18.5923 by 2 we get the radius which is 9.29617.
The area of a circle is given by
. Since we have the radius we can substitute into the equation to obtain
That is, the area is approximately 271.35 square centimeters.
I am not sure how many decimal places you have been asked to round to, but since you did 2 for the digits of pi, I went with two in the answer. Note that along the way you need to carry it out to more than two to avoid something called rounding error.