Question

Find the area of a segment formed by a chord 8" long in a circle with radius of 8"

Answer 1

Draw 2 radii such that their endpoints on the circle are 8 inches apartconnect these points; this is the chord and it is 8 inches longthe 2 radii and the chord form an equilateral triangleeach side is 8 inches and each angle is 60 degreesfind the area of the sector formed by the 2 radiifind the area of the equilateral trianglesubtract the area of the triangle from the area of the sector and you have the area of the segment of the circlearea of the sector: A=(q/360)*∏r2A=(60/360)*∏*82A=(1/6)(∏)(64)A=(64/6)(∏)A=(32/3)(3.14159)A=33.5103 square inchesarea of the triangle:A=(√3/4)a2 where a=length of a sideA=(1.73205/4)(82)A=(1.73205/4)(64)A=(1.73205)(16)A=27.7128 square inchessubtract33.5103-27.7128=5.7975 square inchesthe area of the segment is 5.7975 square inches