how do i find the area of a segment of a circle if given chord of length 8 at a distance of 4 from center

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Tony -Sketching a picture always helps to understand the problem. The yellow in the picture below is the area you want to calculate.  The best approach is determine the area of the whole sector defined by θ, then subtract the area of the triangle AOB. Make sense?Since you know h=4 and AB=8.  Draw a line from O perpendicular to AB.  This line is h=4 and it bisects AB into two segments also equal to 4.  Now you have two isosceles triangle with legs = 4.  That means angle A = angle B = 45 degrees which means angle AOB is 90 degrees.The area of the sector = 90/360 x area of whole circle where area of circle = πr^2.Now the area of the triangle = 1/2(base)(height), where base = 8 and height = 4.I'll leave it for you to figure out the final answer.  Hope this helped