Area of a segment is given by:
Where R = Radius and = angle of the sector if lines were taken from the centre of the circle to the corners of the segment. Note that is in radians.
You do not have the angle yet, but you can find it from your known values (length of radius (R) and perpendicular distance from centre to midpoint of the chord (d)).
Examine the image below:
Now imagine a line d connecting the centre to the midpoint of the chord. This cuts the triangle into two smaller triangles, and also bisects angle .
Look at one of the smaller triangles carefully. You'll see that you have a right angled triangle with two known sides R and d, which is the hypotenuse and the side adjacent to angle respectively
Having derived the angle, you will be able to substitute it into the equation given at the beginning of this post.