the perpendicalar to the chord will be 22.1 inches
and it will meet the chord at its midpoint
So you have a rightangled triangle with the radius as the hypotenuse 6.42 ft or 77.04 inches
and shorter sides 22.1 and x
Use Pythagoras to find the radius
x^2 + 22.1^2 = 77.04^2
-use basic trig to find the central angle of the sector
-use a ration to find the area of the sector
-find the area of the triangle formed by the chord and the centre of the circle, you know the angle
Area of whole circle = 70.04^2 π
subtract the area of the triangle from the area of the sector to find the area of the segment.
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