What is the area of a segment of a circle with a height 6m and the lenght cord 20m ? 8.54,74.6,85.4, 746.6 ??

Question

round off to nearest whole number ..... thx so much !

Answer 1

Draw the sketch.
r^2 = 10^2 + (r - 6)^2
r^2 = 100 + r^2 - 12r + 36
12r = 136
r = 136/12 = 11.33333
θ = 2arc sin(10/11.33333) = 123.855degrees
h = 11.33333 - 6 = 5.33333
b = 20
A(seg) = fractional part of circle - triangle
A(seg) = (123.855/360)( π11.33333^2) - (1/2)(20)(5.33333)
A(seg) = 85.4944m^2 [third choice]