A quarter circle, is as what it name suggests, 1/4 of a circle. To get its area, you must get first the area of the circle as a whole -
A = pi * r^2
= 3.14 * 7cm^2
= 3.14 * 49cm^2
= 153.86cm^2 area of the whole circle
Then, divide the area of the whole circle by 4.
153.86cm^2 / 4 = 38.465cm^2
Therefore, the area of a quarter circle is 38.47cm^2